@misc{BJ24, title={The Ehrhart series of alcoved polytopes}, author={Elisabeth Bullock and Yuhan Jiang}, year={2024}, eprint={2412.02787}, archivePrefix={arXiv}, primaryClass={math.CO}, } @incollection {alcove2, AUTHOR = {Lam, Thomas and Postnikov, Alexander}, TITLE = {Alcoved polytopes {II}}, BOOKTITLE = {Lie groups, geometry, and representation theory}, SERIES = {Progr. Math.}, VOLUME = {326}, PAGES = {253--272}, PUBLISHER = {Birkh\"{a}user/Springer, Cham}, YEAR = {2018}, ISBN = {978-3-030-02190-0; 978-3-030-02191-7}, MRCLASS = {52B12 (05E10 20F55)}, MRNUMBER = {3890212}, MRREVIEWER = {Gabriel\ K.\ Cunningham}, DOI = {10.1007/978-3-030-02191-7\_10}, } @article {alcove1, AUTHOR = {Lam, Thomas and Postnikov, Alexander}, TITLE = {Alcoved polytopes. {I}}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {38}, YEAR = {2007}, NUMBER = {3}, PAGES = {453--478}, MRCLASS = {52B12 (52B40)}, MRNUMBER = {2352704}, MRREVIEWER = {Jes\'{u}s\ A.\ De Loera}, DOI = {10.1007/s00454-006-1294-3}, } @article {AJR20, AUTHOR = {Ayyer, Arvind and Josuat-Verg\`es, Matthieu and Ramassamy, Sanjay}, TITLE = {Extensions of partial cyclic orders and consecutive coordinate polytopes}, JOURNAL = {Ann. H. Lebesgue}, FJOURNAL = {Annales Henri Lebesgue}, VOLUME = {3}, YEAR = {2020}, PAGES = {275--297}, MRCLASS = {52B05 (05A05 05A10 06A75 52B11)}, MRNUMBER = {4113648}, MRREVIEWER = {Lionel\ Pournin}, DOI = {10.5802/ahl.33}, } @article {multihyper, AUTHOR = {Han, Guo-Niu and Josuat-Verg\`es, Matthieu}, TITLE = {Flag statistics from the {E}hrhart {$h^*$}-polynomial of multi-hypersimplices}, JOURNAL = {Electron. J. Combin.}, FJOURNAL = {Electronic Journal of Combinatorics}, VOLUME = {23}, YEAR = {2016}, NUMBER = {1}, PAGES = {Paper 1.55, 20}, MRCLASS = {05E45 (05E05)}, MRNUMBER = {3484760}, MRREVIEWER = {Sam\ Hopkins}, DOI = {10.37236/5538}, URL = {https://doi.org/10.37236/5538}, } @misc{parisi2024magic, title={The Magic Number Conjecture for the $m=2$ amplituhedron and Parke-Taylor identities}, author={Matteo Parisi and Melissa Sherman-Bennett and Ran Tessler and Lauren Williams}, year={2024}, eprint={2404.03026}, archivePrefix={arXiv}, primaryClass={math.CO}, } @misc{postnikov2006, title={Total positivity, Grassmannians, and networks}, author={Alexander Postnikov}, year={2006}, eprint={math/0609764}, archivePrefix={arXiv}, primaryClass={math.CO} } @article {Megiddo1976, AUTHOR = {Megiddo, Nimrod}, TITLE = {Partial and complete cyclic orders}, JOURNAL = {Bull. Amer. Math. Soc.}, FJOURNAL = {Bulletin of the American Mathematical Society}, VOLUME = {82}, YEAR = {1976}, NUMBER = {2}, PAGES = {274--276}, MRCLASS = {06A10}, MRNUMBER = {404065}, MRREVIEWER = {Hartmut\ H\"{o}ft}, DOI = {10.1090/S0002-9904-1976-14020-7}, } @article {flow2023, AUTHOR = {Gonz\'{a}lez D'Le\'{o}n, Rafael S. and Hanusa, Christopher R. H. and Morales, Alejandro H. and Yip, Martha}, TITLE = {Column-convex matrices, {$G$}-cyclic orders, and flow polytopes}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {70}, YEAR = {2023}, NUMBER = {4}, PAGES = {1593--1631}, MRCLASS = {52B05 (05A19 05C50 06A07 11B83 15B48)}, MRNUMBER = {4670370}, DOI = {10.1007/s00454-023-00518-9}, } @article {snake2022, AUTHOR = {von Bell, Matias and Braun, Benjamin and Hanely, Derek and Serhiyenko, Khrystyna and Vega, Julianne and Vindas-Mel\'{e}ndez, Andr\'{e}s R. and Yip, Martha}, TITLE = {Triangulations, order polytopes, and generalized snake posets}, JOURNAL = {Comb. Theory}, FJOURNAL = {Combinatorial Theory}, VOLUME = {2}, YEAR = {2022}, NUMBER = {3}, PAGES = {Paper No. 10, 34}, MRCLASS = {52B20 (06A07 52B05 52B12)}, MRNUMBER = {4498591}, MRREVIEWER = {Manuela\ Muzika Dizdarevi\'{c}}, DOI = {10.5070/c62359166}, } @article {twoposet1986, AUTHOR = {Stanley, Richard P.}, TITLE = {Two poset polytopes}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {1}, YEAR = {1986}, NUMBER = {1}, PAGES = {9--23}, MRCLASS = {52A25 (52A40)}, MRNUMBER = {824105}, MRREVIEWER = {P.\ McMullen}, DOI = {10.1007/BF02187680}, } @article {diaconis13, AUTHOR = {Diaconis, Persi and Wood, Philip Matchett}, TITLE = {Random doubly stochastic tridiagonal matrices}, JOURNAL = {Random Structures Algorithms}, FJOURNAL = {Random Structures \& Algorithms}, VOLUME = {42}, YEAR = {2013}, NUMBER = {4}, PAGES = {403--437}, MRCLASS = {60J05 (60B20)}, MRNUMBER = {3068032}, MRREVIEWER = {Sasha\ Sodin}, DOI = {10.1002/rsa.20452}, } @incollection {dkk12, AUTHOR = {Danilov, Vladimir I. and Karzanov, Alexander V. and Koshevoy, Gleb A.}, TITLE = {Coherent fans in the space of flows in framed graphs}, BOOKTITLE = {24th {I}nternational {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({FPSAC} 2012)}, SERIES = {Discrete Math. Theor. Comput. Sci. Proc.}, VOLUME = {AR}, PAGES = {481--490}, PUBLISHER = {Assoc. Discrete Math. Theor. Comput. Sci., Nancy}, YEAR = {2012}, MRCLASS = {05C21 (05E18)}, MRNUMBER = {2958022}, } @article {stanley80, AUTHOR = {Stanley, Richard P.}, TITLE = {Decompositions of rational convex polytopes}, JOURNAL = {Ann. Discrete Math.}, FJOURNAL = {Annals of Discrete Mathematics}, VOLUME = {6}, YEAR = {1980}, PAGES = {333--342}, MRCLASS = {52A43}, MRNUMBER = {593545}, MRREVIEWER = {P.\ McMullen}, } @book {Schrijver, AUTHOR = {Schrijver, Alexander}, TITLE = {Theory of linear and integer programming}, SERIES = {Wiley-Interscience Series in Discrete Mathematics}, NOTE = {A Wiley-Interscience Publication}, PUBLISHER = {John Wiley \& Sons, Ltd., Chichester}, YEAR = {1986}, PAGES = {xii+471}, MRCLASS = {90C05 (90C10)}, MRNUMBER = {874114}, MRREVIEWER = {J\"{u}rgen\ K\"{o}hler}, } @article {npcomplete, AUTHOR = {Galil, Zvi and Megiddo, Nimrod}, TITLE = {Cyclic ordering is {NP}-complete}, JOURNAL = {Theoret. Comput. Sci.}, FJOURNAL = {Theoretical Computer Science}, VOLUME = {5}, YEAR = {1977/78}, NUMBER = {2}, PAGES = {179--182}, MRCLASS = {68C25}, MRNUMBER = {483648}, DOI = {10.1016/0304-3975(77)90005-6}, URL = {https://doi.org/10.1016/0304-3975(77)90005-6}, } @article {ordermatrices, AUTHOR = {Megiddo, Nimrod}, TITLE = {Mixtures of order matrices and generalized order matrices}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, VOLUME = {19}, YEAR = {1977}, NUMBER = {2}, PAGES = {177--181}, MRCLASS = {05B20}, MRNUMBER = {457255}, MRREVIEWER = {J.\ W.\ Moon}, DOI = {10.1016/0012-365X(77)90032-2}, URL = {https://doi.org/10.1016/0012-365X(77)90032-2}, } @article {weakorder04, AUTHOR = {Fiorini, S. and Fishburn, P. C.}, TITLE = {Weak order polytopes}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, VOLUME = {275}, YEAR = {2004}, NUMBER = {1-3}, PAGES = {111--127}, MRCLASS = {91B14 (52A20 91B08)}, MRNUMBER = {2026279}, DOI = {10.1016/S0012-365X(03)00101-8}, URL = {https://doi.org/10.1016/S0012-365X(03)00101-8}, } @article {fiorinifishburn03, AUTHOR = {Fiorini, Samuel and Fishburn, Peter C.}, TITLE = {Extendability of cyclic orders}, JOURNAL = {Order}, FJOURNAL = {Order. A Journal on the Theory of Ordered Sets and its Applications}, VOLUME = {20}, YEAR = {2003}, NUMBER = {2}, PAGES = {151--171}, MRCLASS = {06A07 (52B12)}, MRNUMBER = {2031192}, MRREVIEWER = {Ivan\ Chajda}, DOI = {10.1023/B:ORDE.0000009252.21331.22}, URL = {https://doi.org/10.1023/B:ORDE.0000009252.21331.22}, } @article {fishburnwoodall99, AUTHOR = {Fishburn, P. C. and Woodall, D. R.}, TITLE = {Cycle orders}, JOURNAL = {Order}, FJOURNAL = {Order. A Journal on the Theory of Ordered Sets and its Applications}, VOLUME = {16}, YEAR = {1999}, NUMBER = {2}, PAGES = {149--164}, MRCLASS = {06A07}, MRNUMBER = {1752172}, MRREVIEWER = {Jean-Paul\ Doignon}, DOI = {10.1023/A:1006381208272}, URL = {https://doi.org/10.1023/A:1006381208272}, } @article {dushnikmiller41, AUTHOR = {Dushnik, Ben and Miller, E. W.}, TITLE = {Partially ordered sets}, JOURNAL = {Amer. J. Math.}, FJOURNAL = {American Journal of Mathematics}, VOLUME = {63}, YEAR = {1941}, PAGES = {600--610}, MRCLASS = {27.2X}, MRNUMBER = {4862}, MRREVIEWER = {G.\ Birkhoff}, DOI = {10.2307/2371374}, URL = {https://doi.org/10.2307/2371374}, } @article {fishburn85, AUTHOR = {Fishburn, Peter C.}, TITLE = {Interval graphs and interval orders}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, VOLUME = {55}, YEAR = {1985}, NUMBER = {2}, PAGES = {135--149}, MRCLASS = {06A10 (05C75)}, MRNUMBER = {798530}, MRREVIEWER = {K.\ P.\ Bogart}, DOI = {10.1016/0012-365X(85)90042-1}, URL = {https://doi.org/10.1016/0012-365X(85)90042-1}, } @book {dimensiontrotter92, AUTHOR = {Trotter, William T.}, TITLE = {Combinatorics and partially ordered sets}, SERIES = {Johns Hopkins Series in the Mathematical Sciences}, NOTE = {Dimension theory}, PUBLISHER = {Johns Hopkins University Press, Baltimore, MD}, YEAR = {1992}, PAGES = {xvi+307}, MRCLASS = {06-02 (05-02 06A06 06A07)}, MRNUMBER = {1169299}, MRREVIEWER = {K.\ P.\ Bogart}, } @article {positroids, AUTHOR = {Ardila, Federico and Rinc\'{o}n, Felipe and Williams, Lauren}, TITLE = {Positroids and non-crossing partitions}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {368}, YEAR = {2016}, NUMBER = {1}, PAGES = {337--363}, MRCLASS = {05B35 (05A15 05A19 46L53)}, MRNUMBER = {3413866}, MRREVIEWER = {Anna\ de Mier}, DOI = {10.1090/tran/6331}, URL = {https://doi.org/10.1090/tran/6331}, } @article {baldonivergne, AUTHOR = {Baldoni, Welleda and Vergne, Mich\`ele}, TITLE = {Kostant partitions functions and flow polytopes}, JOURNAL = {Transform. Groups}, FJOURNAL = {Transformation Groups}, VOLUME = {13}, YEAR = {2008}, NUMBER = {3-4}, PAGES = {447--469}, MRCLASS = {52B12 (05A17 11D45 52C35)}, MRNUMBER = {2452600}, MRREVIEWER = {Jes\'{u}s\ A.\ De Loera}, DOI = {10.1007/s00031-008-9019-8}, URL = {https://doi.org/10.1007/s00031-008-9019-8}, } @article {volume, AUTHOR = {Benedetti, Carolina and Gonz\'{a}lez D'Le\'{o}n, Rafael S. and Hanusa, Christopher R. H. and Harris, Pamela E. and Khare, Apoorva and Morales, Alejandro H. and Yip, Martha}, TITLE = {A combinatorial model for computing volumes of flow polytopes}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {372}, YEAR = {2019}, NUMBER = {5}, PAGES = {3369--3404}, MRCLASS = {05A15 (05A19 05C20 05C21 52A38 52B05 52B11)}, MRNUMBER = {3988614}, MRREVIEWER = {Ruriko\ Yoshida}, DOI = {10.1090/tran/7743}, URL = {https://doi.org/10.1090/tran/7743}, } @article {stanleypitman, AUTHOR = {Stanley, Richard P. and Pitman, Jim}, TITLE = {A polytope related to empirical distributions, plane trees, parking functions, and the associahedron}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {27}, YEAR = {2002}, NUMBER = {4}, PAGES = {603--634}, MRCLASS = {52B11 (05A15 60C05)}, MRNUMBER = {1902680}, MRREVIEWER = {Igor\ Rivin}, DOI = {10.1007/s00454-002-2776-6}, URL = {https://doi.org/10.1007/s00454-002-2776-6}, } @book {BRehrhart, AUTHOR = {Beck, Matthias and Robins, Sinai}, TITLE = {Computing the continuous discretely}, SERIES = {Undergraduate Texts in Mathematics}, EDITION = {Second}, NOTE = {Integer-point enumeration in polyhedra, With illustrations by David Austin}, PUBLISHER = {Springer, New York}, YEAR = {2015}, PAGES = {xx+285}, ISBN = {978-1-4939-2968-9; 978-1-4939-2969-6}, MRCLASS = {11P21 (05A15 05B15 11-02 11H06 52B05 52B20)}, MRNUMBER = {3410115}, DOI = {10.1007/978-1-4939-2969-6}, URL = {https://doi.org/10.1007/978-1-4939-2969-6}, } @article {kostantMM, AUTHOR = {M\'{e}sz\'{a}ros, Karola and Morales, Alejandro H.}, TITLE = {Flow polytopes of signed graphs and the {K}ostant partition function}, JOURNAL = {Int. Math. Res. Not. IMRN}, FJOURNAL = {International Mathematics Research Notices. IMRN}, YEAR = {2015}, NUMBER = {3}, PAGES = {830--871}, MRCLASS = {52B12 (05A15 05C22 52B05)}, MRNUMBER = {3340339}, MRREVIEWER = {Alexander\ I.\ Barvinok}, DOI = {10.1093/imrn/rnt212}, URL = {https://doi.org/10.1093/imrn/rnt212}, } @article{stanleypostnikov, author = {Postnikov, Alexander and Stanley, Richard P.}, title = {Acyclic flow polytopes and Kostant's partition function}, journal = {Conference transparencies}, year = {2000}, link = {https://math.mit.edu/~rstan/transparencies/kostant.pdf} } @article{hypercube, author = {Stanley, Richard P.}, title = {Eulerian partitions of a unit hypercube}, journal = {Proceedings of the NATO Advanced Study Institute}, year = {1977} } @article {Oh, AUTHOR = {Oh, Suho}, TITLE = {Positroids and {S}chubert matroids}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {118}, YEAR = {2011}, NUMBER = {8}, PAGES = {2426--2435}, MRCLASS = {05B35 (52B40)}, MRNUMBER = {2834184}, MRREVIEWER = {Anna\ de Mier}, DOI = {10.1016/j.jcta.2011.06.006}, URL = {https://doi.org/10.1016/j.jcta.2011.06.006}, } @article {NanLi, AUTHOR = {Li, Nan}, TITLE = {Ehrhart {$h^*$}-vectors of hypersimplices}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {48}, YEAR = {2012}, NUMBER = {4}, PAGES = {847--878}, MRCLASS = {52B22 (52A39 52B12)}, MRNUMBER = {3000568}, MRREVIEWER = {Benjamin\ Braun}, DOI = {10.1007/s00454-012-9452-2}, URL = {https://doi.org/10.1007/s00454-012-9452-2}, } @misc{ocneanu2013, title={On the inner structure of a permutation: Bicolored Partitions and Eulerians, Trees and Primitives}, author={Adrian Ocneanu}, year={2013}, eprint={1304.1263}, archivePrefix={arXiv}, primaryClass={math.CO}, } @misc{early2017conjectures, title={Conjectures for Ehrhart $h^*$-vectors of Hypersimplices and Dilated Simplices}, author={Nick Early}, year={2017}, eprint={1710.09507}, archivePrefix={arXiv}, primaryClass={math.CO}, } @article {early2022, AUTHOR = {Early, Nick}, TITLE = {From weakly separated collections to matroid subdivisions}, JOURNAL = {Comb. Theory}, FJOURNAL = {Combinatorial Theory}, VOLUME = {2}, YEAR = {2022}, NUMBER = {2}, PAGES = {Paper No. 2, 35}, MRCLASS = {52B40 (05B35 14T15)}, MRNUMBER = {4449810}, MRREVIEWER = {Gleb\ A.\ Koshevoy}, } @misc{Ocneanu2017, title = {Higher Representation Theory}, url = {https://youtu.be/9gHzFLfPFFU}, journal = {Youtube}, author = {Adrian Ocneanu}, year = 2017, } @article {Kimh*, AUTHOR = {Kim, Donghyun}, TITLE = {A combinatorial formula for the {E}hrhart {$h^\ast$}-vector of the hypersimplex}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {173}, YEAR = {2020}, PAGES = {105213, 15}, MRCLASS = {05E45 (05E10 52B20)}, MRNUMBER = {4056090}, MRREVIEWER = {Hailun\ Zheng}, DOI = {10.1016/j.jcta.2020.105213}, URL = {https://doi.org/10.1016/j.jcta.2020.105213}, } @misc{early2016, title={Combinatorics and Representation Theory for Generalized Permutohedra I: Simplicial Plates}, author={Nick Early}, year={2016}, eprint={1611.06640}, archivePrefix={arXiv}, primaryClass={math.CO}, } @article {Katzman, AUTHOR = {Katzman, Mordechai}, TITLE = {The {H}ilbert series of algebras of the {V}eronese type}, JOURNAL = {Comm. Algebra}, FJOURNAL = {Communications in Algebra}, VOLUME = {33}, YEAR = {2005}, NUMBER = {4}, PAGES = {1141--1146}, MRCLASS = {13A02 (13D40 13H15 14M25)}, MRNUMBER = {2136691}, MRREVIEWER = {David\ E.\ Rush}, DOI = {10.1081/AGB-200053828}, URL = {https://doi.org/10.1081/AGB-200053828}, } @article {AK06, AUTHOR = {Ardila, Federico and Klivans, Caroline J.}, TITLE = {The {B}ergman complex of a matroid and phylogenetic trees}, JOURNAL = {J. Combin. Theory Ser. B}, FJOURNAL = {Journal of Combinatorial Theory. Series B}, VOLUME = {96}, YEAR = {2006}, NUMBER = {1}, PAGES = {38--49}, MRCLASS = {05B35}, MRNUMBER = {2185977}, MRREVIEWER = {Neil\ L.\ White}, DOI = {10.1016/j.jctb.2005.06.004}, URL = {https://doi.org/10.1016/j.jctb.2005.06.004}, } @article {plabictiling, AUTHOR = {Oh, Suho and Postnikov, Alexander and Speyer, David E.}, TITLE = {Weak separation and plabic graphs}, JOURNAL = {Proc. Lond. Math. Soc. (3)}, FJOURNAL = {Proceedings of the London Mathematical Society. Third Series}, VOLUME = {110}, YEAR = {2015}, NUMBER = {3}, PAGES = {721--754}, MRCLASS = {05E15}, MRNUMBER = {3342103}, MRREVIEWER = {Kyungyong\ Lee}, DOI = {10.1112/plms/pdu052} } @article {Carlitz1966, AUTHOR = {Carlitz, L. and Roselle, D. P. and Scoville, R. A.}, TITLE = {Permutations and sequences with repetitions by number of increases}, JOURNAL = {J. Combinatorial Theory}, FJOURNAL = {Journal of Combinatorial Theory}, VOLUME = {1}, YEAR = {1966}, PAGES = {350--374}, MRCLASS = {05.10}, MRNUMBER = {200178}, MRREVIEWER = {John\ Riordan}, } @article {branden08, AUTHOR = {Br{\"a}nd{\'e}n, Petter}, TITLE = {Actions on permutations and unimodality of descent polynomials}, JOURNAL = {European J. Combin.}, FJOURNAL = {European Journal of Combinatorics}, VOLUME = {29}, YEAR = {2008}, NUMBER = {2}, PAGES = {514--531}, MRCLASS = {05A05 (05A15 06A07)}, MRNUMBER = {2388387}, DOI = {10.1016/j.ejc.2006.12.010}, } @article {peterson13twosided, AUTHOR = {Petersen, T. Kyle}, TITLE = {Two-sided {E}ulerian numbers via balls in boxes}, JOURNAL = {Math. Mag.}, FJOURNAL = {Mathematics Magazine}, VOLUME = {86}, YEAR = {2013}, NUMBER = {3}, PAGES = {159--176}, MRCLASS = {05A05}, MRNUMBER = {3063137}, DOI = {10.4169/math.mag.86.3.159} } @article{Foata1965, author = {Dominique Foata}, title = {{\'E}tude alg{\'e}brique de certains probl{\`e}mes d'analyse combinatoire et du calcul des probabilit\'{e}s}, journal = {Annales de l'ISUP}, year = {1965}, volume = {14}, pages = {81--241}, } @article{Claesson2013, author = {Anders Claesson and Brignall Robert}, title = {Turning cycle restrictions into mesh patterns via Foata’s fundamental transformation}, journal = {Journal of Combinatorial Theory, Series A}, volume = {123}, pages = {194--222}, year = {2014}, publisher = {Elsevier}, } @article{oh2017, AUTHOR = {Oh, Suho}, TITLE = {Positroids and {S}chubert matroids}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {118}, YEAR = {2011}, NUMBER = {8}, PAGES = {2426--2435}, DOI = {10.1016/j.jcta.2011.06.006}, URL = {https://doi.org/10.1016/j.jcta.2011.06.006}, } @article {ehrhart, AUTHOR = {Ehrhart, Eug\`ene}, TITLE = {Sur les poly\`edres rationnels homoth\'etiques \`a{} {$n$}\ dimensions}, JOURNAL = {C. R. Acad. Sci. Paris}, FJOURNAL = {Comptes Rendus Hebdomadaires des S\'eances de l'Acad\'emie des Sciences}, VOLUME = {254}, YEAR = {1962}, PAGES = {616--618}, MRCLASS = {10.25 (52.10)}, MRNUMBER = {130860}, } @article {SIF, AUTHOR = {Callan, David}, TITLE = {Counting stabilized-interval-free permutations}, JOURNAL = {J. Integer Seq.}, FJOURNAL = {Journal of Integer Sequences}, VOLUME = {7}, YEAR = {2004}, NUMBER = {1}, PAGES = {Article 04.1.8, 7}, MRCLASS = {05A15 (05A05)}, MRNUMBER = {2049703}, } @article {polyposi, AUTHOR = {Lam, Thomas and Postnikov, Alexander}, TITLE = {Polypositroids}, JOURNAL = {Forum Math. Sigma}, FJOURNAL = {Forum of Mathematics. Sigma}, VOLUME = {12}, YEAR = {2024}, PAGES = {Paper No. e42, 67}, MRCLASS = {52B40 (05B35 20F55)}, MRNUMBER = {4718184}, DOI = {10.1017/fms.2024.11}, URL = {https://doi.org/10.1017/fms.2024.11}, } @incollection {lusztig, AUTHOR = {Lusztig, George}, TITLE = {Introduction to total positivity}, BOOKTITLE = {Positivity in {L}ie theory: open problems}, SERIES = {De Gruyter Exp. Math.}, VOLUME = {26}, PAGES = {133--145}, PUBLISHER = {de Gruyter, Berlin}, YEAR = {1998}, MRCLASS = {20G20 (14P99)}, MRNUMBER = {1648700}, MRREVIEWER = {Vladimir\ L.\ Popov}, } @book {bjornerbrenti, AUTHOR = {Bj{\"o}rner, Anders and Brenti, Francesco}, TITLE = {Combinatorics of {C}oxeter groups}, SERIES = {Graduate Texts in Mathematics}, VOLUME = {231}, PUBLISHER = {Springer, New York}, YEAR = {2005}, PAGES = {xiv+363}, ISBN = {978-3540-442387; 3-540-44238-3}, MRCLASS = {05-01 (05E15 20F55)}, MRNUMBER = {2133266}, MRREVIEWER = {Jian-yi\ Shi}, } @article {bjorner, AUTHOR = {Bj{\"o}rner, Anders}, TITLE = {Some combinatorial and algebraic properties of {C}oxeter complexes and {T}its buildings}, JOURNAL = {Adv. in Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {52}, YEAR = {1984}, NUMBER = {3}, PAGES = {173--212}, MRCLASS = {52A25 (05B35 13H10 20G15)}, MRNUMBER = {744856}, MRREVIEWER = {S.\ Milne}, DOI = {10.1016/0001-8708(84)90021-5}, URL = {https://doi.org/10.1016/0001-8708(84)90021-5}, } @book {bourbaki, AUTHOR = {Bourbaki, N.}, TITLE = {\'El\'ements de math\'ematique. {F}asc. {XXXIV}. {G}roupes et alg\`ebres de {L}ie. {C}hapitre {IV}: {G}roupes de {C}oxeter et syst\`emes de {T}its. {C}hapitre {V}: {G}roupes engendr\'es par des r\'eflexions. {C}hapitre {VI}: syst\`emes de racines}, SERIES = {Actualit\'es Scientifiques et Industrielles [Current Scientific and Industrial Topics]}, VOLUME = {No. 1337}, PUBLISHER = {Hermann, Paris}, YEAR = {1968}, PAGES = {288 pp. (loose errata)}, MRCLASS = {22.50 (17.00)}, MRNUMBER = {240238}, MRREVIEWER = {G.\ B.\ Seligman}, } @book {humphreys, AUTHOR = {Humphreys, James E.}, TITLE = {Reflection groups and {C}oxeter groups}, SERIES = {Cambridge Studies in Advanced Mathematics}, VOLUME = {29}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {1990}, PAGES = {xii+204}, MRCLASS = {20-02 (20F32 20F55 20G15 20H15)}, MRNUMBER = {1066460}, MRREVIEWER = {Louis\ Solomon}, DOI = {10.1017/CBO9780511623646}, URL = {https://doi.org/10.1017/CBO9780511623646}, } @misc{jiang2024ehrhart, title={The Ehrhart $h^*$-polynomial of positroid polytopes}, author={Yuhan Jiang}, year={2024}, eprint={2410.01743}, archivePrefix={arXiv}, primaryClass={math.CO}, } @misc{benedetti2023latticepathmatroidpolytopes, title={On lattice path matroid polytopes: alcoved triangulations and snake decompositions}, author={Carolina Benedetti and Kolja Knauer and Jerónimo Valencia-Porras}, year={2023}, eprint={2303.10458}, archivePrefix={arXiv}, primaryClass={math.CO}, } @article {LPW, AUTHOR = {\L ukowski, Tomasz and Parisi, Matteo and Williams, Lauren K.}, TITLE = {The positive tropical {G}rassmannian, the hypersimplex, and the {$m=2$} amplituhedron}, JOURNAL = {Int. Math. Res. Not. IMRN}, FJOURNAL = {International Mathematics Research Notices. IMRN}, YEAR = {2023}, NUMBER = {19}, PAGES = {16778--16836}, MRCLASS = {14T15 (05B35 14M15 52B05 52B40)}, MRNUMBER = {4651900}, DOI = {10.1093/imrn/rnad010}, URL = {https://doi.org/10.1093/imrn/rnad010}, } @incollection {wil23, AUTHOR = {Williams, Lauren K.}, TITLE = {The positive {G}rassmannian, the amplituhedron, and cluster algebras}, BOOKTITLE = {I{CM}---{I}nternational {C}ongress of {M}athematicians. {V}ol. 6. {S}ections 12--14}, PAGES = {4710--4737}, PUBLISHER = {EMS Press, Berlin}, YEAR = {[2023] \copyright 2023}, ISBN = {978-3-98547-064-8; 978-3-98547-564-3; 978-3-98547-058-7}, MRCLASS = {05E14 (13F60 14J81 14M15 14T15 52B40)}, MRNUMBER = {4680421}, } @article {ahtt, AUTHOR = {Arkani-Hamed, Nima and Thomas, Hugh and Trnka, Jaroslav}, TITLE = {Unwinding the amplituhedron in binary}, JOURNAL = {J. High Energy Phys.}, FJOURNAL = {Journal of High Energy Physics}, YEAR = {2018}, NUMBER = {1}, PAGES = {016, front matter+40}, MRCLASS = {81T60}, MRNUMBER = {3764259}, DOI = {10.1007/jhep01(2018)016}, URL = {https://doi.org/10.1007/jhep01(2018)016}, } @misc{alcovedhstar, title={The Ehrhart series of alcoved polytopes}, author={Elisabeth Bullock and Yuhan Jiang}, year={2024}, eprint={2412.02787}, archivePrefix={arXiv}, primaryClass={math.CO}, } @article {psw, AUTHOR = {Postnikov, Alexander and Speyer, David and Williams, Lauren}, TITLE = {Matching polytopes, toric geometry, and the totally non-negative {G}rassmannian}, JOURNAL = {J. Algebraic Combin.}, FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal}, VOLUME = {30}, YEAR = {2009}, NUMBER = {2}, PAGES = {173--191}, MRCLASS = {20G20 (05B35 13F60 14M25 52B70)}, MRNUMBER = {2525057}, MRREVIEWER = {T.\ Oda}, DOI = {10.1007/s10801-008-0160-1}, URL = {https://doi.org/10.1007/s10801-008-0160-1}, } @article {EKS, AUTHOR = {Elia, Sophia and Kim, Donghyun and Supina, Mariel}, TITLE = {Techniques in equivariant {E}hrhart theory}, JOURNAL = {Ann. Comb.}, FJOURNAL = {Annals of Combinatorics}, VOLUME = {28}, YEAR = {2024}, NUMBER = {3}, PAGES = {819--870}, MRCLASS = {52B20 (05E18)}, MRNUMBER = {4787908}, DOI = {10.1007/s00026-023-00673-z}, URL = {https://doi.org/10.1007/s00026-023-00673-z}, } @misc{CK24, title={Equivariant Ehrhart Theory of Hypersimplices}, author={Oliver Clarke and Max K\"olbl}, year={2025}, eprint={2412.06524}, archivePrefix={arXiv}, primaryClass={math.CO}, } @article {ASV20, AUTHOR = {Ardila, Federico and Supina, Mariel and Vindas-Mel\'endez, Andr\'es R.}, TITLE = {The equivariant {E}hrhart theory of the permutahedron}, JOURNAL = {Proc. Amer. Math. Soc.}, FJOURNAL = {Proceedings of the American Mathematical Society}, VOLUME = {148}, YEAR = {2020}, NUMBER = {12}, PAGES = {5091--5107}, MRCLASS = {52B20 (05E18 14L30 14M25 52B15)}, MRNUMBER = {4163825}, DOI = {10.1090/proc/15113}, URL = {https://doi.org/10.1090/proc/15113}, } @article {ASV21, AUTHOR = {Ardila, Federico and Schindler, Anna and Vindas-Mel\'endez, Andr\'es R.}, TITLE = {The equivariant volumes of the permutahedron}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {65}, YEAR = {2021}, NUMBER = {3}, PAGES = {618--635}, MRCLASS = {52B05 (05A05)}, MRNUMBER = {4226485}, MRREVIEWER = {Mihai\ Cipu}, DOI = {10.1007/s00454-019-00146-2}, URL = {https://doi.org/10.1007/s00454-019-00146-2}, }