%% This BibTeX bibliography file was created using BibDesk. %% http://bibdesk.sourceforge.net/ %% Created for Nicholas Beaton at 2019-05-28 17:29:14 +1000 %% Saved with string encoding Unicode (UTF-8) @article{CW-PNAS, Author = {Corteel, Sylvie and Williams, Lauren K.}, Coden = {PNASFB}, Doi = {10.1073/pnas.0909915107}, Fjournal = {Proceedings of the National Academy of Sciences of the United States of America}, Issn = {1091-6490}, Journal = {Proc. Natl. Acad. Sci. USA}, Mrclass = {05E10 (33C45 33D45 60K35)}, Mrnumber = {2630104 (2011k:05268)}, Mrreviewer = {Tomohiro Sasamoto}, Number = {15}, Pages = {6726--6730}, Title = {Staircase tableaux, the asymmetric exclusion process, and {A}skey-{W}ilson polynomials}, Url = {http://dx.doi.org/10.1073/pnas.0909915107}, Volume = {107}, Year = {2010}, Bdsk-Url-1 = {http://dx.doi.org/10.1073/pnas.0909915107}} @article{CW-Duke1, Author = {Corteel, Sylvie and Williams, Lauren K.}, Coden = {DUMJAO}, Doi = {10.1215/00127094-1433385}, Fjournal = {Duke Mathematical Journal}, Issn = {0012-7094}, Journal = {Duke Math. J.}, Mrclass = {05E10 (33C45 60K35 82C22)}, Mrnumber = {2831874 (2012h:05359)}, Mrreviewer = {Timo Sepp{\"a}l{\"a}inen}, Number = {3}, Pages = {385--415}, Title = {Tableaux combinatorics for the asymmetric exclusion process and {A}skey-{W}ilson polynomials}, Url = {http://dx.doi.org/10.1215/00127094-1433385}, Volume = {159}, Year = {2011}, Bdsk-Url-1 = {http://dx.doi.org/10.1215/00127094-1433385}} @article{CSSW, Author = {Corteel, S. and Stanley, R. and Stanton, D. and Williams, L.}, Coden = {TAMTAM}, Doi = {10.1090/S0002-9947-2012-05588-7}, Fjournal = {Transactions of the American Mathematical Society}, Issn = {0002-9947}, Journal = {Trans. Amer. Math. Soc.}, Mrclass = {05A15 (33C45 82B23)}, Mrnumber = {2946941}, Mrreviewer = {Matthieu Josuat-Verg{\`e}s}, Number = {11}, Pages = {6009--6037}, Title = {Formulae for {A}skey-{W}ilson moments and enumeration of staircase tableaux}, Url = {http://dx.doi.org/10.1090/S0002-9947-2012-05588-7}, Volume = {364}, Year = {2012}, Bdsk-Url-1 = {http://dx.doi.org/10.1090/S0002-9947-2012-05588-7}} @article{CW-Duke2, Author = {Corteel, Sylvie and Williams, Lauren K.}, Doi = {10.1215/00127094-2392422}, Fjournal = {Duke Mathematical Journal}, Issn = {0012-7094}, Journal = {Duke Math. J.}, Mrclass = {05E10 (33C45 60K35 82C22)}, Mrnumber = {3161309}, Number = {15}, Pages = {2987--2996}, Title = {Erratum to ``{T}ableaux combinatorics for the asymmetric exclusion process and {A}skey-{W}ilson polynomials'' [MR2831874]}, Url = {http://dx.doi.org/10.1215/00127094-2392422}, Volume = {162}, Year = {2013}, Bdsk-Url-1 = {http://dx.doi.org/10.1215/00127094-2392422}} @incollection{Koornwinder, Author = {Koornwinder, Tom H.}, Booktitle = {Hypergeometric functions on domains of positivity, {J}ack polynomials, and applications ({T}ampa, {FL}, 1991)}, Doi = {10.1090/conm/138/1199128}, Mrclass = {33D45 (17B20 33D80)}, Mrnumber = {1199128 (94e:33039)}, Mrreviewer = {Eric M. Opdam}, Pages = {189--204}, Publisher = {Amer. Math. Soc., Providence, RI}, Series = {Contemp. Math.}, Title = {Askey-{W}ilson polynomials for root systems of type {$BC$}}, Url = {http://dx.doi.org/10.1090/conm/138/1199128}, Volume = {138}, Year = {1992}, Bdsk-Url-1 = {http://dx.doi.org/10.1090/conm/138/1199128}} @book{Macdonald, Author = {Macdonald, I. G.}, Date-Modified = {2019-05-28 17:24:38 +1000}, Edition = {2}, Isbn = {0-19-853489-2}, Mrclass = {05E05 (05-02 20C30 20C33 20K01 33C80 33D80)}, Mrnumber = {1354144 (96h:05207)}, Mrreviewer = {John R. Stembridge}, Publisher = {The Clarendon Press, Oxford University Press, New York}, Series = {Oxford Mathematical Monographs}, Title = {Symmetric Functions and {H}all Polynomials}, Year = {1995}} @article{Cher1, Author = {Cherednik, Ivan}, Date-Modified = {2019-05-28 17:20:31 +1000}, Doi = {10.1155/S1073792895000341}, Fjournal = {International Mathematics Research Notices}, Issn = {1073-7928}, Journal = {Internat. Math. Res. Notices}, Mrclass = {33D80 (33D45 39A70)}, Mrnumber = {1358032}, Mrreviewer = {Naihuan Jing}, Number = {10}, Pages = {483--515}, Title = {Nonsymmetric {M}acdonald polynomials}, Year = {1995}, Bdsk-Url-1 = {https://doi.org/10.1155/S1073792895000341}} @article{Cher2, Author = {Cherednik, Ivan}, Doi = {10.2307/2118632}, Fjournal = {Annals of Mathematics. Second Series}, Issn = {0003-486X}, Journal = {Ann. of Math. (2)}, Mrclass = {33D80 (05E15 05E35 17B20 39A70)}, Mrnumber = {1314036}, Mrreviewer = {Eric M. Opdam}, Number = {1}, Pages = {191--216}, Title = {Double affine {H}ecke algebras and {M}acdonald's conjectures}, Url = {https://doi.org/10.2307/2118632}, Volume = {141}, Year = {1995}, Bdsk-Url-1 = {https://doi.org/10.2307/2118632}} @article{Opdam, Author = {Opdam, Eric M.}, Doi = {10.1007/BF02392487}, Fjournal = {Acta Mathematica}, Issn = {0001-5962}, Journal = {Acta Math.}, Mrclass = {33C80 (17B99 33D80 43A30)}, Mrnumber = {1353018}, Mrreviewer = {V. A. Golubeva}, Number = {1}, Pages = {75--121}, Title = {Harmonic analysis for certain representations of graded {H}ecke algebras}, Url = {https://doi.org/10.1007/BF02392487}, Volume = {175}, Year = {1995}, Bdsk-Url-1 = {https://doi.org/10.1007/BF02392487}} @manual{sagemath, Author = {{The Sage Developers}}, Key = {SageMath}, Note = {{\tt http://www.sagemath.org}}, Title = {{S}ageMath, the {S}age {M}athematics {S}oftware {S}ystem ({V}ersion v8.2)}, Year = {2018}} @article{Uchiyama, Author = {Uchiyama, Masaru}, Coden = {CSFOEH}, Doi = {10.1016/j.chaos.2006.05.013}, Fjournal = {Chaos, Solitons and Fractals}, Issn = {0960-0779}, Journal = {Chaos Solitons Fractals}, Mrclass = {82C31 (33D45 33D90)}, Mrnumber = {2359487 (2008g:82098)}, Number = {2}, Pages = {398--407}, Title = {Two-species asymmetric simple exclusion process with open boundaries}, Url = {http://dx.doi.org/10.1016/j.chaos.2006.05.013}, Volume = {35}, Year = {2008}, Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.chaos.2006.05.013}} @article{CMW-MLQ, Author = {Corteel, Sylvie and Mandelshtam, Olya and Williams, Lauren}, Note = {arXiv:?}, Title = {From multiline queues to Macdonald polynomials via the exclusion process}, Year = {2018}} @article{KMO15, Author = {Kuniba, Atsuo and Maruyama, Shouya and Okado, Masato}, Doi = {10.1088/1751-8113/48/34/34FT02}, Fjournal = {Journal of Physics. A. Mathematical and Theoretical}, Issn = {1751-8113}, Journal = {J. Phys. A}, Mrclass = {81R12 (17B80 60K35)}, Mrnumber = {3376035}, Mrreviewer = {Julien Bichon}, Number = {34}, Pages = {34FT02, 19}, Title = {Multispecies {TASEP} and combinatorial {$R$}}, Url = {https://doi-org.ezp-prod1.hul.harvard.edu/10.1088/1751-8113/48/34/34FT02}, Volume = {48}, Year = {2015}, Bdsk-Url-1 = {https://doi-org.ezp-prod1.hul.harvard.edu/10.1088/1751-8113/48/34/34FT02}, Bdsk-Url-2 = {https://doi.org/10.1088/1751-8113/48/34/34FT02}} @article{AasLinusson18, Author = {Aas, Erik and Linusson, Svante}, Doi = {10.4171/AIHPD/50}, Fjournal = {Annales de l'Institut Henri Poincar\'{e} D. Combinatorics, Physics and their Interactions}, Issn = {2308-5827}, Journal = {Ann. Inst. Henri Poincar\'{e} D}, Mrclass = {60K35 (82C22)}, Mrnumber = {3760885}, Mrreviewer = {Eunghyun Lee}, Number = {1}, Pages = {127--152}, Title = {Continuous multi-line queues and {TASEP}}, Url = {https://doi-org.ezp-prod1.hul.harvard.edu/10.4171/AIHPD/50}, Volume = {5}, Year = {2018}, Bdsk-Url-1 = {https://doi-org.ezp-prod1.hul.harvard.edu/10.4171/AIHPD/50}, Bdsk-Url-2 = {https://doi.org/10.4171/AIHPD/50}} @article{AyyerLinusson14, Author = {Ayyer, Arvind and Linusson, Svante}, Doi = {10.1016/j.aam.2014.02.001}, Fjournal = {Advances in Applied Mathematics}, Issn = {0196-8858}, Journal = {Adv. in Appl. Math.}, Mrclass = {60K35 (05A05)}, Mrnumber = {3206520}, Mrreviewer = {Halim Zeghdoudi}, Pages = {21--43}, Title = {An inhomogeneous multispecies {TASEP} on a ring}, Url = {https://doi-org.ezp-prod1.hul.harvard.edu/10.1016/j.aam.2014.02.001}, Volume = {57}, Year = {2014}, Bdsk-Url-1 = {https://doi-org.ezp-prod1.hul.harvard.edu/10.1016/j.aam.2014.02.001}, Bdsk-Url-2 = {https://doi.org/10.1016/j.aam.2014.02.001}} @article{Man17, Author = {Mandelshtam, Olya}, Note = {arXiv:1707.02663}, Title = {Toric tableaux and the inhomogeneous two-species TASEP on a ring}, Year = {2017}} @article{KalizeszewskiMorse17, Author = {Kaliszewski, Ryan and Morse, Jennifer}, Note = {arXiv:1710.00801}, Title = {Colorful combinatorics and Macdonald polynomials}, Year = {2017}} @misc{Martin, Author = {Martin, James B.}, Date-Modified = {2019-05-28 17:27:06 +1000}, Eprint = {1810.10650}, Eprinttype = {arxiv}, Title = {Stationary distributions of the multi-type {A}{S}{E}{P}s}, Year = {2018}} @misc{AasGrinbergS, Author = {Aas, Erik and Grinberg, Darij and Scrimshaw, Travis}, Date-Modified = {2019-05-28 17:15:05 +1000}, Eprint = {1810.08157}, Eprinttype = {arxiv}, Title = {Multiline queues with spectral parameters}, Year = {2018}} @article{FerrariMartin, Author = {Ferrari, Pablo A. and Martin, James B.}, Date-Modified = {2019-05-28 17:21:49 +1000}, Doi = {10.1214/009117906000000944}, Fjournal = {The Annals of Probability}, Issn = {0091-1798}, Journal = {Ann. Probab.}, Mrclass = {60K35 (82C22 90B22)}, Mrnumber = {2319708}, Mrreviewer = {C\'edric Bernardin}, Number = {3}, Pages = {807--832}, Title = {Stationary distributions of multi-type totally asymmetric exclusion processes}, Volume = {35}, Year = {2007}, Bdsk-Url-1 = {https://doi.org/10.1214/009117906000000944}} @article{AritaAyyerMallickProlhac12, Author = {Arita, Chikashi and Ayyer, Arvind and Mallick, Kirone and Prolhac, Sylvain}, Date-Modified = {2019-05-28 17:16:24 +1000}, Doi = {10.1088/1751-8113/45/19/195001}, Fjournal = {Journal of Physics. A. Mathematical and Theoretical}, Issn = {1751-8113}, Journal = {J. Phys. A: Math. Theor.}, Mrclass = {82B05}, Mrnumber = {2924494}, Number = {19}, Pages = {195001, 16 pp}, Title = {Generalized matrix ansatz in the multispecies exclusion process---the partially asymmetric case}, Volume = {45}, Year = {2012}, Bdsk-Url-1 = {https://doi.org/10.1088/1751-8113/45/19/195001}} @article{AritaMallick12, Author = {Arita, Chikashi and Mallick, Kirone}, Doi = {10.1088/1751-8113/46/8/085002}, Fjournal = {Journal of Physics. A. Mathematical and Theoretical}, Issn = {1751-8113}, Journal = {J. Phys. A}, Mrclass = {81S22 (15A72 60K35)}, Mrnumber = {3030185}, Mrreviewer = {George M. Tsaklidis}, Number = {8}, Pages = {085002, 11}, Title = {Matrix product solution of an inhomogeneous multi-species {TASEP}}, Url = {https://doi.org/10.1088/1751-8113/46/8/085002}, Volume = {46}, Year = {2013}, Bdsk-Url-1 = {https://doi.org/10.1088/1751-8113/46/8/085002}} @article{EvansFerrariMallick08, Author = {Evans, Martin R. and Ferrari, Pablo A. and Mallick, Kirone}, Date-Modified = {2019-05-28 17:21:38 +1000}, Doi = {10.1007/s10955-009-9696-2}, Fjournal = {Journal of Statistical Physics}, Issn = {0022-4715}, Journal = {J. Stat. Phys.}, Mrclass = {82B31}, Mrnumber = {2505734}, Number = {2}, Pages = {217--239}, Title = {Matrix representation of the stationary measure for the multispecies {TASEP}}, Volume = {135}, Year = {2009}, Bdsk-Url-1 = {https://doi.org/10.1007/s10955-009-9696-2}} @article{ProlhacEvansMallick09, Author = {Prolhac, S. and Evans, M. R. and Mallick, K.}, Date-Modified = {2019-05-28 17:27:45 +1000}, Doi = {10.1088/1751-8113/42/16/165004}, Fjournal = {Journal of Physics. A. Mathematical and Theoretical}, Issn = {1751-8113}, Journal = {J. Phys. A: Math. Theor.}, Mrclass = {60K35}, Mrnumber = {2539272}, Number = {16}, Pages = {165004, 25 pp}, Title = {The matrix product solution of the multispecies partially asymmetric exclusion process}, Volume = {42}, Year = {2009}, Bdsk-Url-1 = {https://doi.org/10.1088/1751-8113/42/16/165004}} @article{DEHP, Author = {Derrida, B. and Evans, M. R. and Hakim, V. and Pasquier, V.}, Coden = {JPHAC5}, Date-Modified = {2019-05-28 17:21:16 +1000}, Fjournal = {Journal of Physics. A. Mathematical and General}, Issn = {0305-4470}, Journal = {J. Phys. A: Math. Gen.}, Mrclass = {60K35 (82C20)}, Mrnumber = {1219679 (94g:60179)}, Mrreviewer = {Pablo A. Ferrari}, Number = {7}, Pages = {1493--1517}, Title = {Exact solution of a {$1$}{D} asymmetric exclusion model using a matrix formulation}, Url = {http://stacks.iop.org/0305-4470/26/1493}, Volume = {26}, Year = {1993}, Bdsk-Url-1 = {http://stacks.iop.org/0305-4470/26/1493}} @article{NPC1, Author = {Zilman, A and Talia, SD and Chait, B and Rout, M and Magnasco, M}, Journal = {PLoS Comput. Biol.}, Title = {Efficiency, selectivity and robustness of the transport through the nuclear pore complex}, Year = {2007}} @article{NPC2, Author = {Zilman, A and Talia, SD and Jovanovic-Talisman, T and Chait, B and Roux, MP and Magnasco, M}, Journal = {PLoS Comput. Biol.}, Title = {Enhancement of Transport Selectivity through Nano-Channels by Non-Specific Competition}, Year = {2010}} @article{bio, Author = {Macdonald, J and Gibbs, J and Pipkin, A}, Date-Modified = {2019-05-28 17:26:29 +1000}, Doi = {10.1002/bip.1968.360060102 }, Journal = {Biopolymers}, Number = {1}, Pages = {1--25}, Title = {Kinetics of biopolymerization on nucleic acid templates}, Volume = {6}, Year = {1968}} @article{Spitzer, Author = {Spitzer, Frank}, Date-Modified = {2019-05-28 17:29:13 +1000}, Doi = {10.1016/0001-8708(70)90034-4}, Fjournal = {Advances in Mathematics}, Issn = {0001-8708}, Journal = {Adv. Math.}, Mrclass = {60.60}, Mrnumber = {0268959 (42 \#3856)}, Mrreviewer = {B. Weiss}, Pages = {246--290 (1970)}, Title = {Interaction of {M}arkov processes}, Volume = {5}, Year = {1970}} @article{vanDiejen, Author = {van Diejen, J. F.}, Coden = {CMPMAF}, Fjournal = {Compositio Mathematica}, Issn = {0010-437X}, Journal = {Compositio Math.}, Mrclass = {39A70 (33C45 33C80 39A12 47B39 81V70)}, Mrnumber = {1313873 (96i:39023)}, Number = {2}, Pages = {183--233}, Title = {Commuting difference operators with polynomial eigenfunctions}, Url = {http://www.numdam.org/item?id=CM_1995__95_2_183_0}, Volume = {95}, Year = {1995}, Bdsk-Url-1 = {http://www.numdam.org/item?id=CM_1995__95_2_183_0}} @article{USW, Author = {Uchiyama, Masaru and Sasamoto, Tomohiro and Wadati, Miki}, Coden = {JPHAC5}, Doi = {10.1088/0305-4470/37/18/006}, Fjournal = {Journal of Physics. A. Mathematical and General}, Issn = {0305-4470}, Journal = {J. Phys. A}, Mrclass = {82C05 (33D45 33D90 82C26)}, Mrnumber = {2065218 (2006d:82047)}, Number = {18}, Pages = {4985--5002}, Title = {Asymmetric simple exclusion process with open boundaries and {A}skey-{W}ilson polynomials}, Url = {http://dx.doi.org/10.1088/0305-4470/37/18/006}, Volume = {37}, Year = {2004}, Bdsk-Url-1 = {http://dx.doi.org/10.1088/0305-4470/37/18/006}} @article{AW, Author = {Askey, Richard and Wilson, James}, Coden = {MAMCAU}, Doi = {10.1090/memo/0319}, Fjournal = {Memoirs of the American Mathematical Society}, Issn = {0065-9266}, Journal = {Mem. Amer. Math. Soc.}, Mrclass = {05A30 (33A65)}, Mrnumber = {783216 (87a:05023)}, Mrreviewer = {Mourad E. H. Ismail}, Number = {319}, Pages = {iv+55}, Title = {Some basic hypergeometric orthogonal polynomials that generalize {J}acobi polynomials}, Url = {http://dx.doi.org/10.1090/memo/0319}, Volume = {54}, Year = {1985}, Bdsk-Url-1 = {http://dx.doi.org/10.1090/memo/0319}} @book{GR, Author = {Gasper, George and Rahman, Mizan}, Doi = {10.1017/CBO9780511526251}, Edition = {Second}, Isbn = {0-521-83357-4}, Mrclass = {33Dxx (05A30 05E35 33-01 33-02)}, Mrnumber = {2128719 (2006d:33028)}, Mrreviewer = {Shaun Cooper}, Note = {With a foreword by Richard Askey}, Pages = {xxvi+428}, Publisher = {Cambridge University Press, Cambridge}, Series = {Encyclopedia of Mathematics and its Applications}, Title = {Basic hypergeometric series}, Url = {http://dx.doi.org/10.1017/CBO9780511526251}, Volume = {96}, Year = {2004}, Bdsk-Url-1 = {http://dx.doi.org/10.1017/CBO9780511526251}} @book{Koekoek, Author = {Koekoek, Roelof and Lesky, Peter A. and Swarttouw, Ren{\'e} F.}, Doi = {10.1007/978-3-642-05014-5}, Isbn = {978-3-642-05013-8}, Mrclass = {33C45 (33-02 33D45)}, Mrnumber = {2656096 (2011e:33029)}, Mrreviewer = {Jeremy Lovejoy}, Note = {With a foreword by Tom H. Koornwinder}, Pages = {xx+578}, Publisher = {Springer-Verlag, Berlin}, Series = {Springer Monographs in Mathematics}, Title = {Hypergeometric orthogonal polynomials and their {$q$}-analogues}, Url = {http://dx.doi.org/10.1007/978-3-642-05014-5}, Year = {2010}, Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-642-05014-5}} @article{BorodinCorwin, Author = {Borodin, Alexei and Corwin, Ivan}, Doi = {10.1007/s00440-013-0482-3}, Fjournal = {Probability Theory and Related Fields}, Issn = {0178-8051}, Journal = {Probab. Theory Related Fields}, Mrclass = {60K35 (33D52 60H15 82B23 82C22)}, Mrnumber = {3152785}, Mrreviewer = {Rongfeng Sun}, Number = {1-2}, Pages = {225--400}, Title = {Macdonald processes}, Url = {http://dx.doi.org/10.1007/s00440-013-0482-3}, Volume = {158}, Year = {2014}, Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00440-013-0482-3}} @inproceedings{CGW-arxiv, Author = {Cantini, Luigi and de Gier, Jan and Wheeler, Michael}, Booktitle = {Proceedings of FPSAC'16}, Date-Modified = {2019-05-28 17:19:13 +1000}, Publisher = {Discrete Math. Theor. Comput. Sci}, Title = {Matrix product and sum rule for {M}acdonald polynomials}, Url = {https://fpsac2016.sciencesconf.org/113732}, Year = {2016}} @article{CGW, Author = {Cantini, Luigi and de Gier, Jan and Wheeler, Michael}, Date-Modified = {2019-05-28 17:16:15 +1000}, Doi = {10.1088/1751-8113/48/38/384001}, Fjournal = {Journal of Physics. A. Mathematical and Theoretical}, Issn = {1751-8113}, Journal = {J. Phys. A: Math. Theor.}, Mrclass = {33D52 (16T25 20C08)}, Mrnumber = {3400909}, Mrreviewer = {Vivek Sahai}, Number = {38}, Pages = {384001, 25 pp}, Title = {Matrix product formula for {M}acdonald polynomials}, Volume = {48}, Year = {2015}, Bdsk-Url-1 = {https://doi.org/10.1088/1751-8113/48/38/384001}} @article{MR3562836, Author = {Cantini, Luigi and Garbali, Alexandr and de Gier, Jan and Wheeler, Michael}, Doi = {10.1088/1751-8113/49/44/444002}, Fjournal = {Journal of Physics. A. Mathematical and Theoretical}, Issn = {1751-8113}, Journal = {J. Phys. A}, Mrclass = {60K35 (33C52 82C20)}, Mrnumber = {3562836}, Number = {44}, Pages = {444002, 23}, Title = {Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries}, Url = {https://doi.org/10.1088/1751-8113/49/44/444002}, Volume = {49}, Year = {2016}, Bdsk-Url-1 = {https://doi.org/10.1088/1751-8113/49/44/444002}} @article{Cantini, Author = {Cantini, Luigi}, Doi = {10.1007/s00023-016-0540-3}, Fjournal = {Annales Henri Poincar\'e. A Journal of Theoretical and Mathematical Physics}, Issn = {1424-0637}, Journal = {Ann. Henri Poincar\'e}, Mrclass = {82C22 (20C08 33C47 60K35)}, Mrnumber = {3626299}, Number = {4}, Pages = {1121--1151}, Title = {Asymmetric simple exclusion process with open boundaries and {K}oornwinder polynomials}, Url = {https://doi.org/10.1007/s00023-016-0540-3}, Volume = {18}, Year = {2017}, Bdsk-Url-1 = {https://doi.org/10.1007/s00023-016-0540-3}} @article{CMW, Author = {Corteel, Sylvie and Mandelshtam, Olya and Williams, Lauren}, Doi = {10.1016/j.aim.2017.09.034}, Fjournal = {Advances in Mathematics}, Issn = {0001-8708}, Journal = {Adv. Math.}, Mrclass = {82C22 (05D40 05E05 05E10 60J10)}, Mrnumber = {3715708}, Mrreviewer = {Konrad P. Pi\'oro}, Pages = {160--204}, Title = {Combinatorics of the two-species {ASEP} and {K}oornwinder moments}, Url = {https://doi.org/10.1016/j.aim.2017.09.034}, Volume = {321}, Year = {2017}, Bdsk-Url-1 = {https://doi.org/10.1016/j.aim.2017.09.034}} @misc{A, Author = {Alexandersson, Per}, Date-Modified = {2019-05-28 17:15:23 +1000}, Eprint = {1602.05153}, Eprinttype = {arxiv}, Title = {Non-symmetric {M}acdonald polynomials and {D}emazure-{L}usztig operators}, Year = {2016}} @unpublished{M-V, Author = {Mandelshtam, Olya and Viennot, Xavier}, Note = {arXiv:1506.01980}, Title = {Tableaux combinatorics of the two-species {PASEP}}, Year = {2015}} @unpublished{k-Mandelshtam, Author = {Mandelshtam, Olya}, Note = {arXiv:1508.04115}, Title = {Matrix ansatz and combinatorics of the k-species {PASEP}}, Year = {2015}} @unpublished{CW-Koornwinder, Author = {Corteel, Sylvie and Williams, Lauren}, Note = {to appear in Selecta Mathematica}, Title = {Macdonald-{K}oornwinder moments and the two-species exclusion process}, Year = {2015}} @incollection{Noumi, Author = {Nakagawa, Jun and Noumi, Masatoshi and Shirakawa, Miki and Yamada, Yasuhiko}, Booktitle = {Physics and combinatorics, 2000 ({N}agoya)}, Doi = {10.1142/9789812810007_0008}, Mrclass = {05E10}, Mrnumber = {1872256 (2002k:05242)}, Mrreviewer = {Eric S. Egge}, Pages = {180--195}, Publisher = {World Sci. Publ., River Edge, NJ}, Title = {Tableau representation for {M}acdonald's ninth variation of {S}chur functions}, Url = {http://dx.doi.org/10.1142/9789812810007_0008}, Year = {2001}, Bdsk-Url-1 = {http://dx.doi.org/10.1142/9789812810007_0008}} @misc{Rains, Author = {Rains, Eric}, Note = {Personal communication, June 2013}} @misc{Haiman, Author = {Haiman, Mark}, Note = {Personal communication, January 2007}} @incollection{HaimanICM, Author = {Haiman, Mark}, Booktitle = {International {C}ongress of {M}athematicians. {V}ol. {III}}, Mrclass = {33D52 (05E05 17B20 33-02)}, Mrnumber = {2275709}, Mrreviewer = {Thomas Fun Yau Lam}, Pages = {843--872}, Publisher = {Eur. Math. Soc., Z\"urich}, Title = {Cherednik algebras, {M}acdonald polynomials and combinatorics}, Year = {2006}} @article{Cherednik1, Author = {Cherednik, Ivan}, Date-Modified = {2019-05-28 17:19:33 +1000}, Doi = {10.1007/BF01243918}, Fjournal = {Inventiones Mathematicae}, Issn = {0020-9910}, Journal = {Invent. Math.}, Mrclass = {17B37 (16W30 17B20 20F36)}, Mrnumber = {1128220}, Mrreviewer = {V. A. Golubeva}, Number = {2}, Pages = {411--431}, Title = {A unification of {K}nizhnik-{Z}amolodchikov and {D}unkl operators via affine {H}ecke algebras}, Volume = {106}, Year = {1991}, Bdsk-Url-1 = {https://doi-org.ezp-prod1.hul.harvard.edu/10.1007/BF01243918}, Bdsk-Url-2 = {https://doi.org/10.1007/BF01243918}} @article{Cherednik2, Author = {Cherednik, Ivan}, Date-Modified = {2019-05-28 17:19:44 +1000}, Doi = {10.1006/aima.1994.1049}, Fjournal = {Advances in Mathematics}, Issn = {0001-8708}, Journal = {Adv. Math.}, Mrclass = {32G34 (33C80 39A70 81T40 82B23)}, Mrnumber = {1275866}, Mrreviewer = {V. A. Golubeva}, Number = {1}, Pages = {65--95}, Title = {Integration of quantum many-body problems by affine {K}nizhnik-{Z}amolodchikov equations}, Volume = {106}, Year = {1994}, Bdsk-Url-1 = {https://doi-org.ezp-prod1.hul.harvard.edu/10.1006/aima.1994.1049}, Bdsk-Url-2 = {https://doi.org/10.1006/aima.1994.1049}} @article{MacdonaldBourbaki, Author = {Macdonald, I. G.}, Fjournal = {Ast\'erisque}, Issn = {0303-1179}, Journal = {Ast\'erisque}, Mrclass = {33D80 (05E05 20C99 33D45)}, Mrnumber = {1423624}, Mrreviewer = {A. Klimyk}, Note = {S\'eminaire Bourbaki, Vol. 1994/95}, Number = {237}, Pages = {Exp. No. 797, 4, 189--207}, Title = {Affine {H}ecke algebras and orthogonal polynomials}, Year = {1996}} @article{KasataniTakeyama, Author = {Kasatani, Masahiro and Takeyama, Yoshihiro}, Date-Modified = {2019-05-28 17:24:05 +1000}, Doi = {10.1619/fesi.50.491}, Fjournal = {Funkcialaj Ekvacioj. Serio Internacia}, Issn = {0532-8721}, Journal = {Funkcial. Ekvac.}, Mrclass = {39A13 (17B69 33C52 33D80 81R12 81R50)}, Mrnumber = {2381328}, Number = {3}, Pages = {491--509}, Title = {The quantum {K}nizhnik-{Z}amolodchikov equation and non-symmetric {M}acdonald polynomials}, Volume = {50}, Year = {2007}, Bdsk-Url-1 = {https://doi-org.ezp-prod1.hul.harvard.edu/10.1619/fesi.50.491}, Bdsk-Url-2 = {https://doi.org/10.1619/fesi.50.491}} @article{Marshall, Author = {Marshall, Dan}, Date-Modified = {2019-05-28 17:26:47 +1000}, Doi = {10.1007/BF01608794}, Fjournal = {Annals of Combinatorics}, Issn = {0218-0006}, Journal = {Ann. Comb.}, Mrclass = {33D52 (05E05)}, Mrnumber = {1772356}, Note = {On combinatorics and statistical mechanics}, Number = {2-4}, Pages = {385--415}, Title = {Symmetric and nonsymmetric {M}acdonald polynomials}, Volume = {3}, Year = {1999}, Bdsk-Url-1 = {https://doi-org.ezp-prod1.hul.harvard.edu/10.1007/BF01608794}, Bdsk-Url-2 = {https://doi.org/10.1007/BF01608794}} @book{MacdonaldAffine, Author = {Macdonald, I. G.}, Doi = {10.1017/CBO9780511542824}, Isbn = {0-521-82472-9}, Mrclass = {33D52 (20C08 33-02)}, Mrnumber = {1976581}, Mrreviewer = {Eric M. Opdam}, Pages = {x+175}, Publisher = {Cambridge University Press, Cambridge}, Series = {Cambridge Tracts in Mathematics}, Title = {Affine {H}ecke algebras and orthogonal polynomials}, Url = {https://doi-org.ezp-prod1.hul.harvard.edu/10.1017/CBO9780511542824}, Volume = {157}, Year = {2003}, Bdsk-Url-1 = {https://doi-org.ezp-prod1.hul.harvard.edu/10.1017/CBO9780511542824}, Bdsk-Url-2 = {https://doi.org/10.1017/CBO9780511542824}} @misc{Viennot, Author = {Viennot, Xavier}, Note = {Slides and video from the talk ``Alternative tableaux, permutations, and partially asymmetric exclusion process,'' at the Isaac Newton Institute, April 23, 2008}} @article{GV, Author = {Gessel, Ira and Viennot, G{\'e}rard}, Coden = {ADMTA4}, Doi = {10.1016/0001-8708(85)90121-5}, Fjournal = {Advances in Mathematics}, Issn = {0001-8708}, Journal = {Adv. in Math.}, Mrclass = {05A15 (05A19)}, Mrnumber = {815360 (87e:05008)}, Mrreviewer = {S. Milne}, Number = {3}, Pages = {300--321}, Title = {Binomial determinants, paths, and hook length formulae}, Url = {http://dx.doi.org/10.1016/0001-8708(85)90121-5}, Volume = {58}, Year = {1985}, Bdsk-Url-1 = {http://dx.doi.org/10.1016/0001-8708(85)90121-5}} @article{Andreief, Author = {Andr\'eief, M.}, Journal = {M\'em. de la Soc. Sci. de Bordeaux}, Pages = {1--14}, Title = {Note sur une relation entre les int\'egrales d\'efinies des produits des fonctions}, Volume = {2}, Year = {1883}} @article{deBruijn, Author = {de Bruijn, N. G.}, Journal = {J. Indian Math. Soc. (N.S.)}, Mrclass = {27.4X}, Mrnumber = {0079647 (18,121g)}, Mrreviewer = {T. Rad{\'o}}, Pages = {133--151 (1956)}, Title = {On some multiple integrals involving determinants}, Volume = {19}, Year = {1955}} @article{Krattenthaler, Author = {Krattenthaler, C.}, Fjournal = {S\'eminaire Lotharingien de Combinatoire}, Issn = {1286-4889}, Journal = {S\'em. Lothar. Combin.}, Mrclass = {05A19 (15A15 33C99)}, Mrnumber = {1701596 (2002i:05013)}, Mrreviewer = {George E. Andrews}, Note = {The Andrews Festschrift (Maratea, 1998)}, Pages = {Art. B42q, 67 pp. (electronic)}, Title = {Advanced determinant calculus}, Volume = {42}, Year = {1999}} @misc{Viennot1, Author = {Viennot, G\'erard}, Note = {Lecture Notes LACIM, UQAM, Montr\'eal, 219 pages, 1984}, Pages = {219 pages}, Title = {Une th\'eorie combinatoire des polynomes orthogonaux}} @incollection{Viennot2, Author = {Viennot, G\'erard}, Booktitle = {Orthogonal polynomials and applications ({B}ar-le-{D}uc, 1984)}, Doi = {10.1007/BFb0076539}, Mrclass = {42C05 (05A15 33A65)}, Mrnumber = {838979 (87g:42046)}, Mrreviewer = {R. A. Askey}, Pages = {139--157}, Publisher = {Springer, Berlin}, Series = {Lecture Notes in Math.}, Title = {A combinatorial theory for general orthogonal polynomials with extensions and applications}, Url = {http://dx.doi.org/10.1007/BFb0076539}, Volume = {1171}, Year = {1985}, Bdsk-Url-1 = {http://dx.doi.org/10.1007/BFb0076539}} @article{KM1, Author = {Karlin, Samuel and McGregor, James}, Fjournal = {Pacific Journal of Mathematics}, Issn = {0030-8730}, Journal = {Pacific J. Math.}, Mrclass = {60.00}, Mrnumber = {0114247 (22 \#5071)}, Mrreviewer = {F. L. Spitzer}, Pages = {1109--1140}, Title = {Coincidence properties of birth and death processes}, Volume = {9}, Year = {1959}} @article{KM2, Author = {Karlin, Samuel and McGregor, James}, Fjournal = {Pacific Journal of Mathematics}, Issn = {0030-8730}, Journal = {Pacific J. Math.}, Mrclass = {60.00}, Mrnumber = {0114248 (22 \#5072)}, Mrreviewer = {F. L. Spitzer}, Pages = {1141--1164}, Title = {Coincidence probabilities}, Volume = {9}, Year = {1959}} @article{Lindstrom, Author = {Lindstr{\"o}m, Bernt}, Fjournal = {The Bulletin of the London Mathematical Society}, Issn = {0024-6093}, Journal = {Bull. London Math. Soc.}, Mrclass = {05B35}, Mrnumber = {0335313 (49 \#95)}, Mrreviewer = {D. J. A. Welsh}, Pages = {85--90}, Title = {On the vector representations of induced matroids}, Volume = {5}, Year = {1973}} @article{Angel, Author = {Angel, Omer}, Coden = {JCBTA7}, Doi = {10.1016/j.jcta.2005.05.004}, Fjournal = {Journal of Combinatorial Theory. Series A}, Issn = {0097-3165}, Journal = {J. Combin. Theory Ser. A}, Mrclass = {82C22 (60K35)}, Mrnumber = {2216456 (2007e:82029)}, Mrreviewer = {Ellen Saada}, Number = {4}, Pages = {625--635}, Title = {The stationary measure of a 2-type totally asymmetric exclusion process}, Url = {http://dx.doi.org/10.1016/j.jcta.2005.05.004}, Volume = {113}, Year = {2006}, Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.jcta.2005.05.004}} @article{BE, Author = {Brak, R. and Essam, J. W.}, Coden = {JPHAC5}, Doi = {10.1088/0305-4470/37/14/002}, Fjournal = {Journal of Physics. A. Mathematical and General}, Issn = {0305-4470}, Journal = {J. Phys. A}, Mrclass = {82B41 (05A15 60K35 82B20)}, Mrnumber = {2066074 (2005f:82040)}, Mrreviewer = {Ira Gessel}, Number = {14}, Pages = {4183--4217}, Title = {Asymmetric exclusion model and weighted lattice paths}, Url = {http://dx.doi.org/10.1088/0305-4470/37/14/002}, Volume = {37}, Year = {2004}, Bdsk-Url-1 = {http://dx.doi.org/10.1088/0305-4470/37/14/002}} @article{BCEPR, Author = {Brak, Richard and Corteel, Sylvie and Essam, John and Parviainen, Robert and Rechnitzer, Andrew}, Fjournal = {Electronic Journal of Combinatorics}, Issn = {1077-8926}, Journal = {Electron. J. Combin.}, Mrclass = {60K35 (60G10)}, Mrnumber = {2274323 (2007j:60164)}, Mrreviewer = {Stuart G. Whittington}, Number = {1}, Pages = {Research Paper 108, 23 pp. (electronic)}, Title = {A combinatorial derivation of the {PASEP} stationary state}, Url = {http://www.combinatorics.org/Volume_13/Abstracts/v13i1r108.html}, Volume = {13}, Year = {2006}, Bdsk-Url-1 = {http://www.combinatorics.org/Volume_13/Abstracts/v13i1r108.html}} @article{CW1, Author = {Corteel, Sylvie and Williams, Lauren K.}, Doi = {10.1016/j.aam.2006.08.002}, Fjournal = {Advances in Applied Mathematics}, Issn = {0196-8858}, Journal = {Adv. in Appl. Math.}, Mrclass = {05E10 (60C05)}, Mrnumber = {2352041 (2008g:05220)}, Mrreviewer = {Mikl{\'o}s B{\'o}na}, Number = {3}, Pages = {293--310}, Title = {Tableaux combinatorics for the asymmetric exclusion process}, Url = {http://dx.doi.org/10.1016/j.aam.2006.08.002}, Volume = {39}, Year = {2007}, Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.aam.2006.08.002}} @article{CW2, Author = {Corteel, Sylvie and Williams, Lauren K.}, Doi = {10.1093/imrn/rnm055}, Fjournal = {International Mathematics Research Notices. IMRN}, Issn = {1073-7928}, Journal = {Int. Math. Res. Not. IMRN}, Mrclass = {60J10 (05A05 05A30)}, Mrnumber = {2354800 (2008i:60124)}, Mrreviewer = {Stuart G. Whittington}, Number = {17}, Pages = {Art. ID rnm055, 27}, Title = {A {M}arkov chain on permutations which projects to the {PASEP}}, Url = {http://dx.doi.org/10.1093/imrn/rnm055}, Year = {2007}, Bdsk-Url-1 = {http://dx.doi.org/10.1093/imrn/rnm055}} @article{shock, Author = {Derrida, B. and Lebowitz, J. L. and Speer, E. R.}, Coden = {JSTPSB}, Doi = {10.1007/BF02770758}, Fjournal = {Journal of Statistical Physics}, Issn = {0022-4715}, Journal = {J. Statist. Phys.}, Mrclass = {82C22 (60K35)}, Mrnumber = {1492490 (99f:82049)}, Mrreviewer = {Pablo A. Ferrari}, Note = {Dedicated to Bernard Jancovici}, Number = {1-2}, Pages = {135--167}, Title = {Shock profiles for the asymmetric simple exclusion process in one dimension}, Url = {http://dx.doi.org/10.1007/BF02770758}, Volume = {89}, Year = {1997}, Bdsk-Url-1 = {http://dx.doi.org/10.1007/BF02770758}} @article{jumping, Author = {Duchi, Enrica and Schaeffer, Gilles}, Coden = {JCBTA7}, Doi = {10.1016/j.jcta.2004.09.006}, Fjournal = {Journal of Combinatorial Theory. Series A}, Issn = {0097-3165}, Journal = {J. Combin. Theory Ser. A}, Mrclass = {60K35 (05A15 82C22)}, Mrnumber = {2128962 (2006c:60130)}, Mrreviewer = {E. J. Janse van Rensburg}, Number = {1}, Pages = {1--29}, Title = {A combinatorial approach to jumping particles}, Url = {http://dx.doi.org/10.1016/j.jcta.2004.09.006}, Volume = {110}, Year = {2005}, Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.jcta.2004.09.006}} @article{Flajolet, Author = {Flajolet, P.}, Coden = {DSMHA4}, Doi = {10.1016/0012-365X(80)90050-3}, Fjournal = {Discrete Mathematics}, Issn = {0012-365X}, Journal = {Discrete Math.}, Mrclass = {05A10 (05A15 30B70)}, Mrnumber = {592851 (82f:05002a)}, Mrreviewer = {L. Carlitz}, Number = {2}, Pages = {125--161}, Title = {Combinatorial aspects of continued fractions}, Url = {http://dx.doi.org/10.1016/0012-365X(80)90050-3}, Volume = {32}, Year = {1980}, Bdsk-Url-1 = {http://dx.doi.org/10.1016/0012-365X(80)90050-3}} @article{Foata, Author = {Foata, Dominique}, Fjournal = {Journal of Combinatorial Theory. Series A}, Journal = {J. Combinatorial Theory Ser. A}, Mrclass = {05A10 (10A40)}, Mrnumber = {0498167 (58 \#16322)}, Mrreviewer = {L. Carlitz}, Number = {3}, Pages = {367--376}, Title = {A combinatorial proof of the {M}ehler formula}, Volume = {24}, Year = {1978}} @article{ISV, Author = {Ismail, Mourad E. H. and Stanton, Dennis and Viennot, G{\'e}rard}, Doi = {10.1016/S0195-6698(87)80046-X}, Fjournal = {European Journal of Combinatorics}, Issn = {0195-6698}, Journal = {European J. Combin.}, Mrclass = {33A65 (05A15 05A30)}, Mrnumber = {930175 (89h:33015)}, Mrreviewer = {Kevin W. J. Kadell}, Number = {4}, Pages = {379--392}, Title = {The combinatorics of {$q$}-{H}ermite polynomials and the {A}skey-{W}ilson integral}, Url = {http://dx.doi.org/10.1016/S0195-6698(87)80046-X}, Volume = {8}, Year = {1987}, Bdsk-Url-1 = {http://dx.doi.org/10.1016/S0195-6698(87)80046-X}} @incollection{IS, Author = {Ismail, Mourad E. H. and Stanton, Dennis}, Booktitle = {Mathematical essays in honor of {G}ian-{C}arlo {R}ota ({C}ambridge, {MA}, 1996)}, Mrclass = {33C45 (05E35)}, Mrnumber = {1627382 (99f:33011)}, Mrreviewer = {Mizan Rahman}, Pages = {377--396}, Publisher = {Birkh\"auser Boston, Boston, MA}, Series = {Progr. Math.}, Title = {More orthogonal polynomials as moments}, Volume = {161}, Year = {1998}} @article{KSZ1, Author = {Kasraoui, Anisse and Stanton, Dennis and Zeng, Jiang}, Doi = {10.1016/j.aam.2010.04.008}, Fjournal = {Advances in Applied Mathematics}, Issn = {0196-8858}, Journal = {Adv. in Appl. Math.}, Mrclass = {05A18 (05A15 05A30 33D45)}, Mrnumber = {2803800 (2012d:05059)}, Mrreviewer = {J. E. Cigler}, Number = {2}, Pages = {216--239}, Title = {The combinatorics of {A}l-{S}alam--{C}hihara {$q$}-{L}aguerre polynomials}, Url = {http://dx.doi.org/10.1016/j.aam.2010.04.008}, Volume = {47}, Year = {2011}, Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.aam.2010.04.008}} @article{MSW, Author = {de M{\'e}dicis, Anne and Stanton, Dennis and White, Dennis}, Coden = {JCBTA7}, Doi = {10.1016/0097-3165(95)90108-6}, Fjournal = {Journal of Combinatorial Theory. Series A}, Issn = {0097-3165}, Journal = {J. Combin. Theory Ser. A}, Mrclass = {05E35 (05A18 05A30 33D45)}, Mrnumber = {1309153 (96b:05177)}, Mrreviewer = {Christian Krattenthaler}, Number = {1}, Pages = {87--114}, Title = {The combinatorics of {$q$}-{C}harlier polynomials}, Url = {http://dx.doi.org/10.1016/0097-3165(95)90108-6}, Volume = {69}, Year = {1995}, Bdsk-Url-1 = {http://dx.doi.org/10.1016/0097-3165(95)90108-6}} @article{Sasamoto, Author = {Sasamoto, Tomohiro}, Coden = {JPHAC5}, Doi = {10.1088/0305-4470/32/41/306}, Fjournal = {Journal of Physics. A. Mathematical and General}, Issn = {0305-4470}, Journal = {J. Phys. A}, Mrclass = {82B20 (33D45 33D90 82B26)}, Mrnumber = {1732546 (2000k:82025)}, Number = {41}, Pages = {7109--7131}, Title = {One-dimensional partially asymmetric simple exclusion process with open boundaries: orthogonal polynomials approach}, Url = {http://dx.doi.org/10.1088/0305-4470/32/41/306}, Volume = {32}, Year = {1999}, Bdsk-Url-1 = {http://dx.doi.org/10.1088/0305-4470/32/41/306}} @article{SZ, Author = {Shapiro, Louis W. and Zeilberger, Doron}, Coden = {JMBLAJ}, Doi = {10.1007/BF00275693}, Fjournal = {Journal of Mathematical Biology}, Issn = {0303-6812}, Journal = {J. Math. Biol.}, Mrclass = {92A05 (60J10)}, Mrnumber = {684944 (84f:92011)}, Mrreviewer = {Petr K{\.u}rka}, Number = {3}, Pages = {351--357}, Title = {A {M}arkov chain occurring in enzyme kinetics}, Url = {http://dx.doi.org/10.1007/BF00275693}, Volume = {15}, Year = {1982}, Bdsk-Url-1 = {http://dx.doi.org/10.1007/BF00275693}} @incollection{Viennot-book, Author = {Viennot, G{\'e}rard}, Booktitle = {Orthogonal polynomials and applications ({B}ar-le-{D}uc, 1984)}, Doi = {10.1007/BFb0076539}, Mrclass = {42C05 (05A15 33A65)}, Mrnumber = {838979 (87g:42046)}, Mrreviewer = {R. A. Askey}, Pages = {139--157}, Publisher = {Springer, Berlin}, Series = {Lecture Notes in Math.}, Title = {A combinatorial theory for general orthogonal polynomials with extensions and applications}, Url = {http://dx.doi.org/10.1007/BFb0076539}, Volume = {1171}, Year = {1985}, Bdsk-Url-1 = {http://dx.doi.org/10.1007/BFb0076539}} @article{Ansatz1, Author = {Derrida, B. and Janowsky, S. A. and Lebowitz, J. L. and Speer, E. R.}, Fjournal = {Journal of Statistical Physics}, Issn = {0022-4715}, Journal = {J. Statist. Phys.}, Mrclass = {60K35 (82C20)}, Mrnumber = {1251221}, Mrreviewer = {Pablo A. Ferrari}, Number = {5-6}, Pages = {813--842}, Title = {Exact solution of the totally asymmetric simple exclusion process: shock profiles}, Url = {https://doi.org/10.1007/BF01052811}, Volume = {73}, Year = {1993}, Bdsk-Url-1 = {https://doi.org/10.1007/BF01052811}} @article{Ayyer2, Author = {Arita, Chikashi and Ayyer, Arvind and Mallick, Kirone and Prolhac, Sylvain}, Doi = {10.1088/1751-8113/45/19/195001}, Fjournal = {Journal of Physics. A. Mathematical and Theoretical}, Issn = {1751-8113}, Journal = {J. Phys. A}, Mrclass = {82B05}, Mrnumber = {2924494}, Number = {19}, Pages = {195001, 16}, Title = {Generalized matrix ansatz in the multispecies exclusion process---the partially asymmetric case}, Url = {http://dx.doi.org/10.1088/1751-8113/45/19/195001}, Volume = {45}, Year = {2012}, Bdsk-Url-1 = {http://dx.doi.org/10.1088/1751-8113/45/19/195001}} @article{Ayyer1, Author = {Ayyer, Arvind and Lebowitz, Joel L. and Speer, Eugene R.}, Doi = {10.1007/s10955-009-9724-2}, Fjournal = {Journal of Statistical Physics}, Issn = {0022-4715}, Journal = {J. Stat. Phys.}, Mrclass = {82C22 (60K35)}, Mrnumber = {2548602 (2010i:82127)}, Mrreviewer = {M{\'a}rton Bal{\'a}zs}, Number = {5-6}, Pages = {1009--1037}, Title = {On the two species asymmetric exclusion process with semi-permeable boundaries}, Url = {http://dx.doi.org/10.1007/s10955-009-9724-2}, Volume = {135}, Year = {2009}, Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10955-009-9724-2}} @article{Ayyer3, Author = {Ayyer, A. and Lebowitz, J. L. and Speer, E. R.}, Fjournal = {Markov Processes and Related Fields}, Issn = {1024-2953}, Journal = {Markov Process. Related Fields}, Mrclass = {82C22 (60K35)}, Mrnumber = {2952023}, Number = {1}, Pages = {157--176}, Title = {On some classes of open two-species exclusion processes}, Volume = {18}, Year = {2012}} @article{Corteel, Author = {Corteel, Sylvie}, Doi = {10.1016/j.aam.2006.01.006}, Fjournal = {Advances in Applied Mathematics}, Issn = {0196-8858}, Journal = {Adv. in Appl. Math.}, Mrclass = {05A05 (05A15 33D15)}, Mrnumber = {2290808 (2007j:05003)}, Mrreviewer = {Mikl{\'o}s B{\'o}na}, Number = {2}, Pages = {149--163}, Title = {Crossings and alignments of permutations}, Url = {http://dx.doi.org/10.1016/j.aam.2006.01.006}, Volume = {38}, Year = {2007}, Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.aam.2006.01.006}} @article{ER, Author = {Essler, Fabian H. L. and Rittenberg, Vladimir}, Coden = {JPHAC5}, Doi = {10.1088/0305-4470/29/13/013}, Fjournal = {Journal of Physics. A. Mathematical and General}, Issn = {0305-4470}, Journal = {J. Phys. A}, Mrclass = {82B20 (17B81 81R10 82B23)}, Mrnumber = {1400161 (97b:82017)}, Number = {13}, Pages = {3375--3407}, Title = {Representations of the quadratic algebra and partially asymmetric diffusion with open boundaries}, Url = {http://dx.doi.org/10.1088/0305-4470/29/13/013}, Volume = {29}, Year = {1996}, Bdsk-Url-1 = {http://dx.doi.org/10.1088/0305-4470/29/13/013}} @article{Sandow, Author = {Sandow, S. and Sch{\"u}tz, G.}, Doi = {10.1209/0295-5075/26/1/002}, Fjournal = {Europhysics Letters}, Issn = {0295-5075}, Journal = {Europhys. Lett.}, Mrclass = {82C20 (81R50)}, Mrnumber = {1269168 (95a:82071)}, Number = {1}, Pages = {7--12}, Title = {On {$U\sb q[{\rm SU}(2)]$}-symmetric driven diffusion}, Url = {http://dx.doi.org/10.1209/0295-5075/26/1/002}, Volume = {26}, Year = {1994}, Bdsk-Url-1 = {http://dx.doi.org/10.1209/0295-5075/26/1/002}} @article{traffic, Author = {Schreckenberg, D. and Wolf, D.}, Journal = {Traffic and Granular Flow}, Year = {1997}} @article{SS, Author = {Simion, R. and Stanton, D.}, Coden = {JCAMDI}, Doi = {10.1016/0377-0427(95)00250-2}, Fjournal = {Journal of Computational and Applied Mathematics}, Issn = {0377-0427}, Journal = {J. Comput. Appl. Math.}, Mrclass = {33D45 (05A15 05A30 05E35)}, Mrnumber = {1418763 (98b:33038)}, Mrreviewer = {Jiang Zeng}, Number = {1-2}, Pages = {297--329}, Title = {Octabasic {L}aguerre polynomials and permutation statistics}, Url = {http://dx.doi.org/10.1016/0377-0427(95)00250-2}, Volume = {68}, Year = {1996}, Bdsk-Url-1 = {http://dx.doi.org/10.1016/0377-0427(95)00250-2}} @article{HHL3, Author = {Haglund, J. and Haiman, M. and Loehr, N.}, Coden = {AJMAAN}, Date-Modified = {2019-05-28 17:23:15 +1000}, Doi = {10.1353/ajm.2008.0015}, Fjournal = {American Journal of Mathematics}, Issn = {0002-9327}, Journal = {Amer. J. Math.}, Mrclass = {05E05}, Mrnumber = {2405160 (2009f:05262)}, Mrreviewer = {Pavlo Pylyavskyy}, Number = {2}, Pages = {359--383}, Title = {A combinatorial formula for nonsymmetric {M}acdonald polynomials}, Volume = {130}, Year = {2008}, Bdsk-Url-1 = {http://dx.doi.org/10.1353/ajm.2008.0015}} @article{HHL2, Author = {Haglund, J. and Haiman, M. and Loehr, N.}, Coden = {PNASFB}, Date-Modified = {2019-05-28 17:23:04 +1000}, Doi = {10.1073/pnas.0408497102}, Fjournal = {Proceedings of the National Academy of Sciences of the United States of America}, Issn = {1091-6490}, Journal = {Proc. Natl. Acad. Sci. USA}, Mrclass = {05E05}, Mrnumber = {2141666 (2006g:05223b)}, Mrreviewer = {Frank Sottile}, Number = {8}, Pages = {2690--2696}, Title = {Combinatorial theory of {M}acdonald polynomials. {I}. {P}roof of {H}aglund's formula}, Volume = {102}, Year = {2005}, Bdsk-Url-1 = {http://dx.doi.org/10.1073/pnas.0408497102}} @article{HHL1, Author = {Haglund, J. and Haiman, M. and Loehr, N.}, Date-Modified = {2019-05-28 17:22:50 +1000}, Doi = {10.1090/S0894-0347-05-00485-6}, Fjournal = {Journal of the American Mathematical Society}, Issn = {0894-0347}, Journal = {J. Amer. Math. Soc.}, Mrclass = {05E05}, Mrnumber = {2138143 (2006g:05223a)}, Mrreviewer = {Frank Sottile}, Number = {3}, Pages = {735--761}, Title = {A combinatorial formula for {M}acdonald polynomials}, Volume = {18}, Year = {2005}, Bdsk-Url-1 = {http://dx.doi.org/10.1090/S0894-0347-05-00485-6}} @article{HaimanHilbert, Author = {Haiman, Mark}, Date-Modified = {2019-05-28 17:23:27 +1000}, Doi = {10.1090/S0894-0347-01-00373-3}, Fjournal = {Journal of the American Mathematical Society}, Issn = {0894-0347}, Journal = {J. Amer. Math. Soc.}, Mrclass = {14C05 (05E05 20C30 33D45)}, Mrnumber = {1839919}, Mrreviewer = {Claudio Procesi}, Number = {4}, Pages = {941--1006}, Title = {Hilbert schemes, polygraphs and the {M}acdonald positivity conjecture}, Volume = {14}, Year = {2001}, Bdsk-Url-1 = {https://doi-org.ezp-prod1.hul.harvard.edu/10.1090/S0894-0347-01-00373-3}, Bdsk-Url-2 = {https://doi.org/10.1090/S0894-0347-01-00373-3}} @article{Schwer, Author = {Schwer, Christoph}, Date-Modified = {2019-05-28 17:28:18 +1000}, Doi = {10.1155/IMRN/2006/75395}, Fjournal = {International Mathematics Research Notices}, Issn = {1073-7928}, Journal = {Int. Math. Res. Not.}, Mrclass = {22E50 (05E05 17B20 20C08)}, Mrnumber = {2264725}, Mrreviewer = {Arun Ram}, Pages = {Art. ID 75395, 31 pp}, Title = {Galleries, {H}all-{L}ittlewood polynomials, and structure constants of the spherical {H}ecke algebra}, Year = {2006}, Bdsk-Url-1 = {https://doi.org/10.1155/IMRN/2006/75395}} @article{Lenart, Author = {Lenart, Cristian}, Date-Modified = {2019-05-28 17:24:15 +1000}, Doi = {10.1016/j.aim.2008.09.007}, Fjournal = {Advances in Mathematics}, Issn = {0001-8708}, Journal = {Adv. Math.}, Mrclass = {05E05 (33D52)}, Mrnumber = {2462843}, Mrreviewer = {Xinrong Ma}, Number = {1}, Pages = {324--340}, Title = {On combinatorial formulas for {M}acdonald polynomials}, Volume = {220}, Year = {2009}, Bdsk-Url-1 = {https://doi-org.ezp-prod1.hul.harvard.edu/10.1016/j.aim.2008.09.007}, Bdsk-Url-2 = {https://doi.org/10.1016/j.aim.2008.09.007}} @article{RamYip, Author = {Ram, Arun and Yip, Martha}, Date-Modified = {2019-05-28 17:28:01 +1000}, Doi = {10.1016/j.aim.2010.06.022}, Fjournal = {Advances in Mathematics}, Issn = {0001-8708}, Journal = {Adv. Math.}, Mrclass = {05E05 (33D52)}, Mrnumber = {2735761}, Mrreviewer = {Remy Y. Denis}, Number = {1}, Pages = {309--331}, Title = {A combinatorial formula for {M}acdonald polynomials}, Volume = {226}, Year = {2011}, Bdsk-Url-1 = {https://doi-org.ezp-prod1.hul.harvard.edu/10.1016/j.aim.2010.06.022}, Bdsk-Url-2 = {https://doi.org/10.1016/j.aim.2010.06.022}} @book{Liggett, Author = {Liggett, Thomas M.}, Isbn = {3-540-22617-6}, Mrclass = {60-02 (60K35 82C22)}, Mrnumber = {2108619 (2006b:60003)}, Mrreviewer = {Michael Pr{\"a}hofer}, Note = {Reprint of the 1985 original}, Pages = {xvi+496}, Publisher = {Springer-Verlag, Berlin}, Series = {Classics in Mathematics}, Title = {Interacting particle systems}, Year = {2005}} @article{Liggett2, Author = {Liggett, Thomas M.}, Fjournal = {Transactions of the American Mathematical Society}, Issn = {0002-9947}, Journal = {Trans. Amer. Math. Soc.}, Mrclass = {60K35}, Mrnumber = {0410986 (53 \#14726)}, Mrreviewer = {Richard Holley}, Pages = {237--261}, Title = {Ergodic theorems for the asymmetric simple exclusion process}, Volume = {213}, Year = {1975}} @book{Liggett3, Author = {Liggett, Thomas M.}, Doi = {10.1007/978-3-662-03990-8}, Isbn = {3-540-65995-1}, Mrclass = {60K35 (82B21 82C21 91B12)}, Mrnumber = {1717346 (2001g:60247)}, Mrreviewer = {Ellen Saada}, Pages = {xii+332}, Publisher = {Springer-Verlag, Berlin}, Series = {Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]}, Title = {Stochastic interacting systems: contact, voter and exclusion processes}, Url = {http://dx.doi.org/10.1007/978-3-662-03990-8}, Volume = {324}, Year = {1999}, Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-662-03990-8}} @phdthesis{thesis, Author = {Ferreira, Jeffrey Paul}, Date-Modified = {2019-05-28 17:22:26 +1000}, Eprint = {1303.3619}, Eprinttype = {arxiv}, School = {UC Davis}, Title = {Row-strict quasisymmetric Schur functions, characterizations of Demazure atoms, and permuted basement nonsymmetric {M}acdonald polynomials}, Year = {2011}, Bdsk-Url-1 = {https://arxiv.org/pdf/1303.3619.pdf}}