%% This BibTeX bibliography file was created using BibDesk. %% https://bibdesk.sourceforge.io/ %% Created for Raman Sanyal at 2024-11-11 17:28:11 +0100 %% Saved with string encoding Unicode (UTF-8) @book{barvinok, author = {Barvinok, Alexander}, date-added = {2024-11-11 17:28:07 +0100}, date-modified = {2024-11-11 17:28:11 +0100}, doi = {10.1090/gsm/054}, mrclass = {52-02 (49N15 52-01 90-02 90C05 90C22 90C25)}, mrnumber = {1940576}, mrreviewer = {P.\ McMullen}, pages = {x+366 pp.}, publisher = {American Mathematical Society, Providence, RI}, series = {Graduate Studies in Mathematics}, title = {A course in convexity}, volume = {54}, year = {2002}, bdsk-url-1 = {https://doi.org/10.1090/gsm/054}} @book{Knuth, author = {Knuth, Donald E.}, date-added = {2024-06-02 15:58:16 +0200}, date-modified = {2024-06-02 15:58:19 +0200}, mrclass = {68A50}, mrnumber = {445948}, mrreviewer = {M.\ Muller}, note = {Sorting and searching}, pages = {xi+722 pp. (1 foldout)}, publisher = {Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont.}, series = {Addison-Wesley Series in Computer Science and Information Processing}, title = {The art of computer programming. {V}olume 3}, year = {1973}} @article{GenPermOrig, author = {Postnikov, A.}, journal = {International Mathematics Research Notices}, number = {6}, pages = {1026--1106}, publisher = {OUP}, title = {Permutohedra, associahedra, and beyond}, volume = {2009}, year = {2009}} @article{GenPermFaces, 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} } @phdthesis{AlexThesis, author = {Black, A.}, school = {University of California, Davis}, title = {Monotone Paths on Polytopes: Combinatorics and Optimization}, year = {2024}} @article{HighDimRookWalk, author = {Kauers, M. and Zeilberger, D.}, fjournal = {Advances in Applied Mathematics}, journal = {Adv. in Appl. Math.}, number = {4}, pages = {813--819}, publisher = {Elsevier}, title = {The computational challenge of enumerating high-dimensional rook walks}, volume = {47}, year = {2011}, DOI = {10.1016/j.aam.2011.03.004}, } @article{PartitionedPermutahedra, AUTHOR = {Horiguchi, Tatsuya and Masuda, Mikiya and Shareshian, John and Song, Jongbaek}, TITLE = {Toric orbifolds associated with partitioned weight polytopes in classical types}, JOURNAL = {Selecta Math. (N.S.)}, FJOURNAL = {Selecta Mathematica. New Series}, VOLUME = {30}, YEAR = {2024}, NUMBER = {5}, PAGES = {Paper No. 84, 37 pp.}, DOI = {10.1007/s00029-024-00977-9}, URL = {https://doi.org/10.1007/s00029-024-00977-9}, } @article{Removahedra, author = {Pilaud, Vincent}, journal = {Revista Colombiana de Matem{\'a}ticas}, number = {1}, pages = {21--42}, publisher = {Universidad Nacional de Colombia y Sociedad Colombiana de Matem{\'a}ticas}, title = {Which nestohedra are removahedra?}, volume = {51}, year = {2017}} @article{PilesofCubes, author = {Athanasiadis, C.}, journal = {Discrete \& Computational Geometry}, pages = {117--130}, publisher = {Springer}, title = {Piles of cubes, monotone path polytopes, and hyperplane arrangements}, volume = {21}, year = {1999}} @inproceedings{VolumeSharpPHard, author = {Brightwell, G. and Winkler, P.}, booktitle = {STOC '91: Proceedings of the twenty-third annual ACM symposium on Theory of computing}, pages = {175--181}, title = {Counting linear extensions is {\#}P-complete}, year = {1991}, doi = {10.1145/103418.103441}, } @article{AFApplication, author = {Stanley, R.}, fjournal = {Journal of Combinatorial Theory, Series A}, journal = {J. Combin. Theory Ser. A}, number = {1}, pages = {56--65}, publisher = {Academic Press}, title = {Two combinatorial applications of the Aleksandrov-Fenchel inequalities}, volume = {31}, year = {1981}, DOI = {10.1016/0097-3165(81)90053-4}, } @article{PosetAssociahedra, AUTHOR = {Galashin, Pavel}, TITLE = {{$P$}-associahedra}, JOURNAL = {Selecta Math. (N.S.)}, FJOURNAL = {Selecta Mathematica. New Series}, VOLUME = {30}, YEAR = {2024}, NUMBER = {1}, PAGES = {Paper No. 6, 34 pp.}, DOI = {10.1007/s00029-023-00896-1}, URL = {https://doi.org/10.1007/s00029-023-00896-1}, } @incollection{MarkedPosetPolytopes, AUTHOR = {Ardila, Federico and Bliem, Thomas and Salazar, Dido}, TITLE = {Gelfand-{T}setlin polytopes and {F}eigin-{F}ourier-{L}ittelmann-{V}inberg polytopes as marked poset polytopes}, BOOKTITLE = {({FPSAC} 2011)}, SERIES = {{Discrete Math. Theor. Comput. Sci. Proc.}}, VOLUME = {AO}, PAGES = {27--37}, YEAR = {2011}, } @article{OrderPolytopes, author = {Stanley, R.}, fjournal = {Discrete \& Computational Geometry}, journal = {Discrete Comput. Geom.}, number = {1}, pages = {9--23}, publisher = {Springer}, title = {Two poset polytopes}, volume = {1}, year = {1986}, DOI = {10.1007/BF02187680}, } @inproceedings{SleatorTarjanThurston, author = {Sleator, Daniel Dominic and Tarjan, Robert Endre and Thurston, William P}, booktitle = {Proceedings of the eighteenth annual ACM symposium on Theory of computing}, pages = {122--135}, title = {Rotation distance, triangulations, and hyperbolic geometry}, year = {1986}} @article{ClusterBook, author = {Fomin, Sergey and Zelevinsky, Andrei}, journal = {Journal of the American mathematical society}, number = {2}, pages = {497--529}, title = {Cluster algebras I: foundations}, volume = {15}, year = {2002}} @article{OrderPolyAdj, author = {Combarro, E. and Miranda, P.}, journal = {Fuzzy Sets and Systems}, number = {5}, pages = {619--641}, publisher = {Elsevier}, title = {Adjacency on the order polytope with applications to the theory of fuzzy measures}, volume = {161}, year = {2010}} @book{GKZ, AUTHOR = {Gelfand, I. M. and Kapranov, M. M. and Zelevinsky, A. V.}, TITLE = {Discriminants, resultants and multidimensional determinants}, SERIES = {Modern Birkh\"auser Classics}, NOTE = {Reprint of the 1994 edition}, PUBLISHER = {Birkh\"auser Boston, Inc., {Boston, MA}}, YEAR = {2008}, PAGES = {x+523 pp.}, } @article{edmondsorig, author = {Edmonds, Jack}, journal = {Combinatorial Structures and Their Applications}, pages = {69--87}, title = {Submodular functions, matroids, and certain polyhedra}, year = {1970}} @misc{FlagMatAlgGeo, author = {Amanda Cameron and Rodica Dinu and Mateusz Micha{\l}ek and Tim Seynnaeve}, eprint = {arXiv:1811.00272}, title = {Flag matroids: algebra and geometry}, year = {2018}} @article{Hypersimps, author = {Manecke, Sebastian and Sanyal, Raman and So, Jeonghoon}, issue = {3}, journal = {The Electronic Journal of Combinatorics}, title = {S-hypersimplices, pulling triangulations, and monotone paths}, volume = {27}, year = {2020}} @article{FlagPolymatroids, AUTHOR = {Black, Alexander E. and Sanyal, Raman}, TITLE = {Underlying flag polymatroids}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {453}, YEAR = {2024}, PAGES = {Paper No. 109835, 42 pp.}, DOI = {10.1016/j.aim.2024.109835}, URL = {https://doi.org/10.1016/j.aim.2024.109835}, } @article{PostnikovXRays, author = {Bebeacua, Cecilia and Mansour, Toufik and Postnikov, Alex and Severini, Simone}, journal = {Electronic Notes in Discrete Mathematics}, pages = {193--203}, publisher = {Elsevier}, title = {On the X-rays of permutations}, volume = {20}, year = {2005}} @article{Xrayspreprint, author = {Nordh, Gustav}, journal = {arXiv preprint arXiv:1707.03928}, title = {A note on X-rays of permutations and a problem of Brualdi and Fritscher}, year = {2017}} @book{ToricVars, author = {Cox, David A and Little, John B and Schenck, Henry K}, publisher = {American Mathematical Soc.}, title = {Toric varieties}, volume = {124}, year = {2011}} @book{CoxeterMat, author = {Borovik, A. V. and Gelfand, I. M. and White, N.}, booktitle = {Coxeter Matroids}, publisher = {Springer}, title = {Coxeter matroids}, year = {2003}} @article{AsymptoticNumberofScoreSequences, author = {Kolesnik, B.}, journal = {Combinatorica}, number = {4}, pages = {827--844}, publisher = {Springer}, title = {The asymptotic number of score sequences}, volume = {43}, year = {2023}} @article{CellString, author = {Billera, L. and Kapranov, M. and Sturmfels, B.}, fjournal = {Proceedings of the American Mathematical Society}, journal = {Proc. Amer. Math. Soc.}, number = {2}, pages = {549--555}, title = {Cellular strings on polytopes}, volume = {122}, year = {1994}, DOI = {10.2307/2161048}, } @article{flagmats, author = {Borovik, A. V and Gelfand, I. M. and Vince, A. and White, N.}, journal = {Annals of Combinatorics}, number = {1}, pages = {17--26}, publisher = {Springer}, title = {The lattice of flats and its underlying flag matroid polytope}, volume = {1}, year = {1997}} @article{nestsets, author = {Feichtner, E.M. and Sturmfels, B.}, journal = {Portugaliae Mathematica (N.S.)}, pages = {437 -- 468}, title = {Matroid polytopes, nested sets, and {B}ergman fans}, volume = {62}, year = {2005}} @article{StanleyLogConcavity, author = {Stanley, R.}, fjournal = {Journal of Combinatorial Theory, Series A}, journal = {J. Combin. Theory Ser. A}, number = {1}, pages = {56--65}, publisher = {Academic Press}, title = {Two combinatorial applications of the Aleksandrov-Fenchel inequalities}, volume = {31}, year = {1981}, doi = {10.1016/0097-3165(81)90053-4}} @inproceedings{brightwellwinkler, author = {Brightwell, G. and Winkler, P.}, booktitle = {STOC '91: Proceedings of the twenty-third annual ACM symposium on Theory of computing}, pages = {175--181}, title = {Counting linear extensions is {\#}P-complete}, year = {1991}, doi = {10.1145/103418.103441}, } @phdthesis{ASackThesis, author = {Sack, Andrew Ian}, school = {UCLA}, title = {The Combinatorics of Poset Associahedra}, year = {2024}} @article{PassociahedraStackSort, author = {Nguyen, Son and Sack, Andrew}, journal = {arXiv preprint arXiv:2310.02512}, title = {Poset associahedra and stack-sorting}, year = {2023}} @article{PAssociahedraRealization, author = {Sack, A.}, journal = {arXiv preprint arXiv:2301.11449}, title = {A realization of poset associahedra}, year = {2023}} @article{DisconnectedFlipGraph, author = {Liu, G.}, fjournal = {Discrete \& Computational Geometry}, journal = {Discrete Comput. Geom.}, pages = {810--842}, publisher = {Springer}, title = {A zonotope and a product of two simplices with disconnected flip graphs}, volume = {59}, year = {2018}} @article{DisconnectedFlipGraph2, author = {Liu, G.}, fjournal = {Discrete \& Computational Geometry}, journal = {Discrete Comput. Geom.}, number = {1}, pages = {1--30}, publisher = {Springer}, title = {Flip-Connectivity of Triangulations of the Product of a Tetrahedron and Simplex}, volume = {63}, year = {2020}} @article{NonregularProductofSimps, author = {De Loera, J.}, fjournal = {Discrete \& Computational Geometry}, journal = {Discrete Comput. Geom.}, number = {3}, pages = {253--264}, publisher = {Springer}, title = {Nonregular triangulations of products of simplices}, volume = {15}, year = {1996}} @article{HessenbergTools, author = {Precup, M.}, fjournal = {Transformation Groups}, journal = {Transform. Groups}, pages = {491--499}, publisher = {Springer}, title = {The Betti numbers of regular Hessenberg varieties are palindromic}, volume = {23}, year = {2018}} @article{ClosureProblemOriginal, author = {Picard, J.-C.}, journal = {Management science}, number = {11}, pages = {1268--1272}, publisher = {INFORMS}, title = {Maximal closure of a graph and applications to combinatorial problems}, volume = {22}, year = {1976}} @article{PolyhedralCayleyTrick, author = {Huber, B. and Rambau, J. and G{\'o}mez-P{\'e}rez, D.}, fjournal = {Journal of the European Mathematical Society}, journal = {J. Eur. Math. Soc. (JEMS)}, number = {2}, pages = {179--198}, title = {The Cayley trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings}, volume = {2}, year = {2000}} @article{SparseResultantNewtonPolytope, author = {Sturmfels, B.}, journal = {Journal of Algebraic Combinatorics}, pages = {207--236}, publisher = {Kluwer Academic Publishers-Plenum Publishers}, title = {On the Newton polytope of the resultant}, volume = {3}, year = {1994}} @misc{PartitionedPerm2, author = {Horiguchi, T. and Masuda, M. and Sato, T. and Shareshian, J. and Song, J.}, eprint = {2405.09242}, eprinttype = {arxiv}, title = {The representation of $\mathfrak{S}_n$ on the cohomology of the permutohedral variety and gamma vectors of partitioned permutohedra}, year = {2024}} @article{partperms, author = {Heuer, Dylan and Striker, Jessica}, doi = {10.1137/21M1417958}, eprint = {https://doi.org/10.1137/21M1417958}, journal = {SIAM Journal on Discrete Mathematics}, number = {4}, pages = {2863-2888}, title = {Partial Permutation and Alternating Sign Matrix Polytopes}, url = {https://doi.org/10.1137/21M1417958}, volume = {36}, year = {2022}, bdsk-url-1 = {https://doi.org/10.1137/21M1417958}} @book{BauesOriginal, author = {Baues, H.}, publisher = {American Mathematical Soc.}, title = {Geometry of loop spaces and the cobar construction}, volume = {230}, year = {1980}} @article{double_posets, AUTHOR = {Chappell, Thomas and Friedl, Tobias and Sanyal, Raman}, TITLE = {Two double poset polytopes}, JOURNAL = {SIAM J. Discrete Math.}, FJOURNAL = {SIAM Journal on Discrete Mathematics}, VOLUME = {31}, YEAR = {2017}, NUMBER = {4}, PAGES = {2378--2413}, DOI = {10.1137/16M1091800}, URL = {https://doi.org/10.1137/16M1091800}, } @article{BSFiberPoly, author = {Billera, L. and Sturmfels, B.}, fjournal = {Annals of Mathematics. Second Series}, journal = {Ann. of Math. (2)}, mrclass = {52B05 (52B12 52B35)}, mrnumber = {1166643}, mrreviewer = {P. McMullen}, number = {3}, pages = {527--549}, title = {Fiber polytopes}, volume = {135}, year = {1992}, DOI = {10.2307/2946575},} @article{VanderbeiMallows, author = {Mallows, Colin and Vanderbei, Robert J}, journal = {Journal of Integer Sequences}, title = {Which {Y}oung tableaux can represent an outer sum?}, year = {2015}} @article{polymatadj, author = {Topkis, Donald M}, journal = {Mathematical Programming}, number = {2}, pages = {229--237}, publisher = {Springer}, title = {Adjacency on polymatroids}, volume = {30}, year = {1984}} @phdthesis{edmanthesis, author = {Edman, Robert B.}, school = {University of Minnesota}, title = {Diameter and Coherence of Monotone Path Graphs in Low Corank}, year = {2015}} @misc{lineuppolys, archiveprefix = {arXiv}, author = {Federico Castillo and Jean-Philippe Labb{\'e} and Julia Liebert and Arnau Padrol and Eva Philippe and Christian Schilling}, eprint = {2105.06459}, primaryclass = {quant-ph}, title = {An effective solution to convex $1$-body $N$-representability}, year = {2021}} @article{ZonotopeCoherence, AUTHOR = {Edman, Rob and Jiradilok, Pakawut and Liu, Gaku and McConville, Thomas}, TITLE = {Zonotopes whose cellular strings are all coherent}, JOURNAL = {European J. Combin.}, FJOURNAL = {European Journal of Combinatorics}, VOLUME = {96}, YEAR = {2021}, PAGES = {Paper No. 103352, 18 pp.}, DOI = {10.1016/j.ejc.2021.103352}, URL = {https://doi.org/10.1016/j.ejc.2021.103352}, } @article{GKZResultantPaper, author = {Gelfand, I. and Kapranov, M. and Zelevinsky, A.}, fjournal = {Advances in Mathematics}, journal = {Adv. Math.}, number = {2}, pages = {237--254}, publisher = {Academic Press}, title = {Newton polytopes of the classical resultant and discriminant}, volume = {84}, year = {1990}} @article{colorfultriangulations, AUTHOR = {Acharya, Rohan and M\"utze, Torsten and Verciani, Francesco}, TITLE = {Flips in colorful triangulations}, JOURNAL = {J. Comput. Geom.}, FJOURNAL = {Journal of Computational Geometry}, VOLUME = {16}, YEAR = {2025}, NUMBER = {1}, PAGES = {295--332}, doi = {10.20382/jocg.v16i1a9}, } @article{dConnectedFlipGraph, author = {Athanasiadis, C. and Edelman, P. and Reiner, V.}, fjournal = {Mathematische Zeitschrift}, journal = {Math. Z.}, number = {2}, pages = {315--334}, publisher = {Springer}, title = {Monotone paths on polytopes}, volume = {235}, year = {2000}, DOI = {10.1007/s002090000152}, } @misc{MonotonePathFlipConnectivity, author = {Gaetz, Christian and Hersh, Patricia}, eprint = {2410.08076}, eprinttype = {arxiv}, title = {Poset topology, moves, and Bruhat interval polytope lattices}, year = {2024}} @article{ShadowsofOrderPolytopes, author = {Eppstein, D.}, journal = {ACM Transactions on Algorithms (TALG)}, number = {1}, pages = {1--22}, publisher = {ACM New York, NY, USA}, title = {The parametric closure problem}, volume = {14}, year = {2017}} @article{HershHirsch, author = {Hersh, P.}, fjournal = {Discrete \& Computational Geometry}, journal = {Discrete Comput. Geom.}, pages = {1--30}, publisher = {Springer}, title = {Posets arising as 1-skeleta of simple polytopes, the nonrevisiting path conjecture, and poset topology}, year = {2023}} @book{zieglerbook, author = {Ziegler, G. M.}, publisher = {Springer Science \& Business Media}, title = {Lectures on polytopes}, volume = {152}, year = {2012}} @article{PivotPoly, author = {A. E. Black and J. A. De Loera and N. L\"{u}tjeharms and R. Sanyal}, journal = {arXiv:2201.05134}, title = {The Polyhedral Geometry of Pivot Rules and Monotone Paths}, year = {2022}} @article{sweeppolys, author = {Padrol A. and Philippe E.}, journal = {arXiv:2102.06134}, title = {Sweeps, polytopes, oriented matroids, and allowable graphs of permutations}, year = {2021}} @inproceedings{grasspolysubdivs, author = {Postnikov, A.}, booktitle = {Proceedings of the International Congress of Mathematicians}, pages = {3167 -- 3196}, title = {Positive {G}rassmannians and Polyhedral Subdivisions}, volume = {3}, year = {2018}} @book{fujishige_submodular_2005, abstract = {Satoru Fujishige, 990017588270302884}, author = {Fujishige, Satoru}, edition = {2. ed.}, keywords = {Combinatorial optimization, Fonctions sous modulaires, Kombinatorische Optimierung, Optimisation combinatoire, Submodular functions, Submodulare Funktion}, language = {eng}, publisher = {Amsterdam ua: Elsevier}, series = {Annals of discrete mathematics {BV004511910} 58}, title = {Submodular functions and optimization}, year = {2005}} @article{claesson_counting_2023, abstract = {Advancing research. Creating connections.}, author = {Claesson, Anders and Dukes, Mark and Frankl{\'\i}n, Atli and Stef{\'a}nsson, Sigurður}, doi = {10.1090/proc/16425}, issn = {0002-9939, 1088-6826}, journal = {Proc. Amer. Math. Soc.}, language = {en}, number = {09}, pages = {3691--3704}, title = {Counting tournament score sequences}, volume = {151}, year = {2023}} @article{NewtonPolytopesSurvey, author = {Monical, C. and Tokcan, N. and Yong, A.}, journal = {Selecta Mathematica}, number = {5}, pages = {66}, publisher = {Springer}, title = {Newton polytopes in algebraic combinatorics}, volume = {25}, year = {2019}} @article{ErdosScoreSequences, author = {Erd\H{o}s, P. and Ginzburg, A. and Ziv, A.}, journal = {Bull. Res. Council Israel F}, number = {1}, pages = {41--43}, publisher = {Citeseer}, title = {Theorem in the additive number theory}, volume = {10}, year = {1961}} @article{landau_dominance_1953, AUTHOR = {Landau, H. G.}, TITLE = {On dominance relations and the structure of animal societies. {III}. {T}he condition for a score structure}, JOURNAL = {Bull. Math. Biophys.}, FJOURNAL = {The Bulletin of Mathematical Biophysics}, VOLUME = {15}, YEAR = {1953}, PAGES = {143--148}, DOI = {10.1007/bf02476378}, URL = {https://doi.org/10.1007/bf02476378}, } @article{moon_extension_1963, author = {Moon, John}, journal = {Pacific J. Math.}, language = {en}, number = {4}, pages = {1343--1345}, title = {An extension of {Landau}'s theorem on tournaments}, volume = {13}, year = {1963}} @book{moon_topics_2013, author = {Moon, John W.}, copyright = {Public domain in the USA.}, keywords = {Tournaments (Graph theory)}, language = {Englisch}, month = may, title = {Topics on {Tournaments}}, url = {https://www.gutenberg.org/ebooks/42833}, urldate = {2023-07-17}, year = {2013}, bdsk-url-1 = {https://www.gutenberg.org/ebooks/42833}} @misc{reid_landaus_2015, abstract = {We give a new proof of the sufficiency of Landau's conditions for a non-decreasing sequence of integers to be the score sequence of a tournament. The proof involves jumping down a total order on sequences satisfying Landau's conditions and provides a \$O(n{\textasciicircum}2)\$ algorithm that can be used to construct a tournament whose score sequence is any in the total order. We also compare this algorithm with to other algorithms that jump along this total order, one jumping down and one jumping up.}, author = {Reid, K. B. and Santana, M.}, doi = {10.48550/arXiv.1509.04205}, keywords = {05C20, Mathematics - Combinatorics}, month = sep, note = {arXiv:1509.04205 [math]}, publisher = {arXiv}, title = {Landau's {Theorem} {Revisited} {Again}}, url = {http://arxiv.org/abs/1509.04205}, urldate = {2024-02-14}, year = {2015}, bdsk-url-1 = {http://arxiv.org/abs/1509.04205}, bdsk-url-2 = {https://doi.org/10.48550/arXiv.1509.04205}} @misc{oeis_foundation_inc_-line_2024, key = {OEIS}, title = {The {On}-{Line} {Encyclopedia} of {Integer} {Sequences} ({OEIS})}, shorttitle = {{OEIS}}, author = {{OEIS Foundation Inc. (2024)}}, note = {Published electronically at \url{https://oeis.org}}, }