@incollection {Stanley1998, AUTHOR = {Stanley, Richard P.}, TITLE = {Hyperplane arrangements, parking functions and tree inversions}, BOOKTITLE = {Mathematical essays in honor of {G}ian-{C}arlo {R}ota ({C}ambridge, {MA}, 1996)}, SERIES = {Progr. Math.}, VOLUME = {161}, PAGES = {359--375}, PUBLISHER = {Birkh\"{a}user Boston, Boston, MA}, YEAR = {1998}, MRCLASS = {05A15 (52B30)}, MRNUMBER = {1627378}, MRREVIEWER = {Volkmar Welker}, } @incollection {Stanley1997, AUTHOR = {Stanley, Richard P.}, TITLE = {Parking functions and noncrossing partitions}, NOTE = {The Wilf Festschrift (Philadelphia, PA, 1996)}, JOURNAL = {Electron. J. Combin.}, FJOURNAL = {Electronic Journal of Combinatorics}, VOLUME = {4}, YEAR = {1997}, NUMBER = {2}, PAGES = {Research Paper 20, approx. 14 pp.}, MRCLASS = {05A17 (05E05)}, MRNUMBER = {1444167}, DOI = {10.37236/1335}, URL = {https://doi.org/10.37236/1335}, } @article {Chassaing2001, AUTHOR = {Chassaing, Philippe and Marckert, Jean-Fran\c{c}ois}, TITLE = {Parking functions, empirical processes, and the width of rooted labeled trees}, JOURNAL = {Electron. J. Combin.}, FJOURNAL = {Electronic Journal of Combinatorics}, VOLUME = {8}, YEAR = {2001}, NUMBER = {1}, PAGES = {Research Paper 14, 19 pp.}, MRCLASS = {05C05 (60C05 60F15)}, MRNUMBER = {1814521}, MRREVIEWER = {Zbigniew Palka}, DOI = {10.37236/1558}, URL = {https://doi.org/10.37236/1558}, } @article {carr2005coxetercomplexes, AUTHOR = {Carr, Michael P. and Devadoss, Satyan L.}, TITLE = {Coxeter complexes and graph-associahedra}, JOURNAL = {Topology Appl.}, FJOURNAL = {Topology and its Applications}, VOLUME = {153}, YEAR = {2006}, NUMBER = {12}, PAGES = {2155--2168}, MRCLASS = {52B11 (05B45 14H10 14P25)}, MRNUMBER = {2239078}, MRREVIEWER = {Seth Sullivant}, DOI = {10.1016/j.topol.2005.08.010}, URL = {https://doi.org/10.1016/j.topol.2005.08.010}, } @article{stanley2020question, author = {Stanley, Richard P.}, title = {Problem 12191, Problems and Solutions}, journal = {The American Mathematical Monthly}, volume = {127}, number = {6}, pages = {563--571}, year = {2020}, publisher = {Taylor \& Francis}, doi = {10.1080/00029890.2020.1747921}, URL = {https://doi.org/10.1080/00029890.2020.1747921}, } @article {vonbell2024flowpolytopes, AUTHOR = {Bell, Matias von and Braun, Benjamin and Bruegge, Kaitlin and Hanely, Derek and Peterson, Zachery and Serhiyenko, Khrystyna and Yip, Martha}, TITLE = {Triangulations of flow polytopes, ample framings, and gentle algebras}, JOURNAL = {Selecta Math. (N.S.)}, FJOURNAL = {Selecta Mathematica. New Series}, VOLUME = {30}, YEAR = {2024}, NUMBER = {3}, PAGES = {Paper No. 55, 34 pp.}, MRCLASS = {52B20 (05C20 05C21 05E45 16G20 52B05)}, MRNUMBER = {4754385}, DOI = {10.1007/s00029-024-00942-6}, URL = {https://doi.org/10.1007/s00029-024-00942-6}, } @book{sagan2013symmetric, title={The symmetric group: representations, combinatorial algorithms, and symmetric functions}, author={Sagan, Bruce E}, edition = {second}, volume={203}, year={2001}, publisher={Springer Science \& Business Media} } @book {macdonald1998symmetric, AUTHOR = {Macdonald, I. G.}, TITLE = {Symmetric functions and {H}all polynomials}, SERIES = {Oxford Classic Texts in the Physical Sciences}, EDITION = {Second}, PUBLISHER = {The Clarendon Press, Oxford University Press, New York}, YEAR = {2015}, PAGES = {xii+475}, MRCLASS = {05E05 (01A75 05-02 20C30 20C33 20K01 33C80 33D80)}, MRNUMBER = {3443860}, } @article{littlewood1934group, title={Group characters and algebra}, author={Littlewood, Dudley Ernest and Richardson, Archibald Read}, journal={Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character}, volume={233}, number={721-730}, pages={99--141}, year={1934}, publisher={The Royal Society London} } @article {fulton2000eigenvalues, AUTHOR = {Fulton, William}, TITLE = {Eigenvalues, invariant factors, highest weights, and {S}chubert calculus}, JOURNAL = {Bull. Amer. Math. Soc. (N.S.)}, FJOURNAL = {American Mathematical Society. Bulletin. New Series}, VOLUME = {37}, YEAR = {2000}, NUMBER = {3}, PAGES = {209--249}, MRCLASS = {15A42 (14L24 14M15 20G05)}, MRNUMBER = {1754641}, MRREVIEWER = {Frank Sottile}, DOI = {10.1090/S0273-0979-00-00865-X}, URL = {https://doi.org/10.1090/S0273-0979-00-00865-X}, } @misc{thawinrak2024, title={A Short Proof for the Polynomiality of the Stretched Littlewood-Richardson Coefficients}, author={Warut Thawinrak}, year={2024}, eprint={2211.06810}, archivePrefix={arXiv}, primaryClass={math.CO}, } @article{Knutson1998, author = "Knutson, Allen and Tao, Terence", title = "{The honeycomb model of $GL_n(\mathbb{C})$ tensor products I: Proof of the saturation conjecture}", doi = "10.1090/s0894-0347-99-00299-4", journal = "J. Am. Math. Soc.", volume = "12", number = "04", pages = "1055--1091", year = "1999" } @article{King2004, author = {King, Ronald and Tollu, Christophe and Toumazet, Frédéric}, year = {2004}, month = {03}, pages = {}, title = {Stretched Littlewood-Richardson and Kostka Coefficients}, volume = {34}, journal = {Symmetry in Physics}, doi = {10.1090/crmp/034/10} } @article {DERKSEN2002, AUTHOR = {Derksen, Harm and Weyman, Jerzy}, TITLE = {On the {L}ittlewood-{R}ichardson polynomials}, JOURNAL = {J. Algebra}, FJOURNAL = {Journal of Algebra}, VOLUME = {255}, YEAR = {2002}, NUMBER = {2}, PAGES = {247--257}, MRCLASS = {16G20 (13A50 13D40 14L24 15A72 20G05)}, MRNUMBER = {1935497}, MRREVIEWER = {M\'{a}ty\'{a}s Domokos}, DOI = {10.1016/S0021-8693(02)00125-4}, URL = {https://doi.org/10.1016/S0021-8693(02)00125-4}, } @article{RASSART2004, title = {A polynomiality property for Littlewood–Richardson coefficients}, journal = {Journal of Combinatorial Theory, Series A}, volume = {107}, number = {2}, pages = {161-179}, year = {2004}, doi = {https://doi.org/10.1016/j.jcta.2004.04.003}, url = {https://www.sciencedirect.com/science/article/pii/S0097316504000536}, author = {Etienne Rassart}, } @article{Ehrhart1962, title={Sur les polyèdres rationnels homothétiques à n dimensions}, author={Ehrhart, Eugène}, journal={C. R. Acad. Sci. Paris}, volume={254}, pages={616--618}, year={1962}, } @article {Sturmfels1995, AUTHOR = {Sturmfels, Bernd}, TITLE = {On vector partition functions}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {72}, YEAR = {1995}, NUMBER = {2}, PAGES = {302--309}, MRCLASS = {52B20 (05A17 14M25)}, MRNUMBER = {1357776}, MRREVIEWER = {Dennis White}, DOI = {10.1016/0097-3165(95)90067-5}, URL = {https://doi.org/10.1016/0097-3165(95)90067-5}, } @misc{hanada2022generalized, title={Generalized parking function polytopes}, author={Mitsuki Hanada and John Lentfer and Andrés R. Vindas-Meléndez}, year={2022}, eprint={2212.06885}, archivePrefix={arXiv}, primaryClass={math.CO} } @article{Konheim1966AnOD, title={An Occupancy Discipline and Applications}, author={Alan G. Konheim and Benjamin Weiss}, journal={Siam Journal on Applied Mathematics}, year={1966}, volume={14}, pages={1266-1274}, url={https://api.semanticscholar.org/CorpusID:123316080} } @misc{behrend2023partial, title={Partial permutohedra}, author={Roger E. Behrend and Federico Castillo and Anastasia Chavez and Alexander Diaz-Lopez and Laura Escobar and Pamela E. Harris and Erik Insko}, year={2023}, eprint={2207.14253}, archivePrefix={arXiv}, primaryClass={math.CO} } @article{CastilloFu2023permutoassociahedron, AUTHOR = {Castillo, Federico and Liu, Fu}, TITLE = {The permuto-associahedron revisited}, JOURNAL = {European J. Combin.}, FJOURNAL = {European Journal of Combinatorics}, VOLUME = {110}, YEAR = {2023}, PAGES = {Paper No. 103706, 30 pp.}, DOI = {10.1016/j.ejc.2023.103706}, URL = {https://doi.org/10.1016/j.ejc.2023.103706}, } @article {Postnikov2006, AUTHOR = {Postnikov, Alex and Reiner, Victor and Williams, Lauren}, TITLE = {Faces of generalized permutohedra}, JOURNAL = {Doc. Math.}, FJOURNAL = {Documenta Mathematica}, VOLUME = {13}, YEAR = {2008}, PAGES = {207--273}, DOI = {10.4171/DM/248} } @article {Postnkov2005, AUTHOR = {Postnikov, Alexander}, TITLE = {Permutohedra, associahedra, and beyond}, JOURNAL = {Int. Math. Res. Not. IMRN}, FJOURNAL = {International Mathematics Research Notices. IMRN}, YEAR = {2009}, NUMBER = {6}, PAGES = {1026--1106}, MRCLASS = {05E30}, MRNUMBER = {2487491}, DOI = {10.1093/imrn/rnn153}, URL = {https://doi.org/10.1093/imrn/rnn153}, } @article{Euretall2024, AUTHOR = {Eur, Christopher and Fink, Alex and Larson, Matt and Spink, Hunter}, TITLE = {Signed permutohedra, delta-matroids, and beyond}, JOURNAL = {Proc. Lond. Math. Soc. (3)}, FJOURNAL = {Proceedings of the London Mathematical Society. Third Series}, VOLUME = {128}, YEAR = {2024}, NUMBER = {3}, PAGES = {Paper No. e12592, 54 pp.}, DOI = {10.1112/plms.12592}, URL = {https://doi.org/10.1112/plms.12592}, } @article {Steinberg1961, AUTHOR = {Steinberg, Robert}, TITLE = {A general {C}lebsch-{G}ordan theorem}, JOURNAL = {Bull. Amer. Math. Soc.}, FJOURNAL = {Bulletin of the American Mathematical Society}, VOLUME = {67}, YEAR = {1961}, PAGES = {406--407}, MRCLASS = {17.30}, MRNUMBER = {126508}, MRREVIEWER = {P. Cartier}, DOI = {10.1090/S0002-9904-1961-10644-7}, URL = {https://doi.org/10.1090/S0002-9904-1961-10644-7}, } @article{Baldoni2008, author = {Baldoni, Velleda and Vergne, Michele}, year = {2008}, month = {12}, pages = {447-469}, title = {Kostant Partitions Functions and Flow Polytopes}, volume = {13}, journal = {Transformation Groups}, doi = {10.1007/s00031-008-9019-8} } @article {mészáros2019, AUTHOR = {M\'{e}sz\'{a}ros, Karola and Morales, Alejandro H.}, TITLE = {Volumes and {E}hrhart polynomials of flow polytopes}, JOURNAL = {Math. Z.}, FJOURNAL = {Mathematische Zeitschrift}, VOLUME = {293}, YEAR = {2019}, NUMBER = {3-4}, PAGES = {1369--1401}, MRCLASS = {52B20 (05C90)}, MRNUMBER = {4024590}, MRREVIEWER = {Matthias Beck}, DOI = {10.1007/s00209-019-02283-z}, URL = {https://doi.org/10.1007/s00209-019-02283-z}, } @article {Corteel2021, AUTHOR = {Corteel, Sylvie and Kim, Jang Soo and M\'{e}sz\'{a}ros, Karola}, TITLE = {Volumes of generalized {C}han-{R}obbins-{Y}uen polytopes}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {65}, YEAR = {2021}, NUMBER = {2}, PAGES = {510--530}, MRCLASS = {52A38}, MRNUMBER = {4212976}, MRREVIEWER = {Denghui Wu}, DOI = {10.1007/s00454-019-00066-1}, URL = {https://doi.org/10.1007/s00454-019-00066-1}, } @misc{Moralesconjecture, author = {Morales, Alejandro}, title = {Examples of Ehrhart Polynomials of Flow Polytopes}, howpublished = {\url{https://sites.google.com/ site/flowpolytopes/ehrhart}} } @article {Amanbayeva_2021, AUTHOR = {Amanbayeva, Aruzhan and Wang, Danielle}, TITLE = {The convex hull of parking functions of length {$n$}}, JOURNAL = {Enumer. Comb. Appl.}, FJOURNAL = {Enumerative Combinatorics and Applications}, VOLUME = {2}, YEAR = {2022}, NUMBER = {2}, PAGES = {Paper No. S2R10, 10 pp.}, MRCLASS = {52B05 (05A15)}, MRNUMBER = {4459984}, MRREVIEWER = {Michael Dougherty}, DOI = {10.54550/eca2022v2s2r10}, URL = {https://doi.org/10.54550/eca2022v2s2r10}, } @article {hanada2024, AUTHOR = {Hanada, Mitsuki and Lentfer, John and Vindas-Mel\'{e}ndez, Andr\'{e}s R.}, TITLE = {Generalized parking function polytopes}, JOURNAL = {Ann. Comb.}, FJOURNAL = {Annals of Combinatorics}, VOLUME = {28}, YEAR = {2024}, NUMBER = {2}, PAGES = {575--613}, MRCLASS = {52B12 (05A15)}, MRNUMBER = {4747488}, DOI = {10.1007/s00026-023-00671-1}, URL = {https://doi.org/10.1007/s00026-023-00671-1}, } @misc{bayer2024parkingfunctionpolytopes, title={Combinatorics of generalized parking-function polytopes}, author={Margaret M. Bayer and Steffen Borgwardt and Teressa Chambers and Spencer Daugherty and Aleyah Dawkins and Danai Deligeorgaki and Hsin-Chieh Liao and Tyrrell McAllister and Angela Morrison and Garrett Nelson and Andrés R. Vindas-Meléndez}, year={2024}, eprint={2403.07387}, archivePrefix={arXiv}, primaryClass={math.CO}, } @book{Stanley2011EC1, AUTHOR = {Stanley, Richard P.}, TITLE = {Enumerative combinatorics. {V}olume 1}, SERIES = {Cambridge Studies in Advanced Mathematics}, VOLUME = {49}, EDITION = {Second edition}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {2012}, PAGES = {xiv+626}, } @inproceedings {edmonds1970, AUTHOR = {Edmonds, J.}, FAUTHOR = {Edmonds, Jack}, TITLE = {Submodular functions, matroids, and certain polyhedra}, BOOKTITLE = {Combinatorial {S}tructures and their {A}pplications ({P}roc. {C}algary {I}nternat. {C}onf., {C}algary, {A}lta., 1969)}, PAGES = {69--87}, PUBLISHER = {Gordon and Breach, New York-London-Paris}, YEAR = {1970}, MRCLASS = {05.35}, MRNUMBER = {270945}, MRREVIEWER = {A. W. Ingleton}, } @article {EurHuhLar2023, AUTHOR = {Eur, C. and Huh, J. and Larson, M.}, FAUTHOR = {Eur, Christopher and Huh, June and Larson, Matt}, TITLE = {Stellahedral geometry of matroids}, JOURNAL = {Forum Math. Pi}, FJOURNAL = {Forum of Mathematics. Pi}, VOLUME = {11}, YEAR = {2023}, PAGES = {Paper No. e24, 48 pp.}, MRCLASS = {14M25 (05B35 14N20 52B40 52C35)}, MRNUMBER = {4653766}, DOI = {10.1017/fmp.2023.24}, URL = {https://doi.org/10.1017/fmp.2023.24}, }