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An International Journal of Mathematics and Computer Science}, VOLUME = {32}, YEAR = {2004}, NUMBER = {4}, PAGES = {437--446}, note = {{\tt arXiv:math.CO/0309332}}, ISSN = {0179-5376}, CODEN = {DCGEER}, MRCLASS = {11D45 (15A36)}, MRNUMBER = {MR2096740}, } @incollection {hardysums, AUTHOR = {Beck, Matthias}, TITLE = {Geometric proofs of polynomial reciprocity laws of {C}arlitz, {B}erndt, and {D}ieter}, BOOKTITLE = {Diophantine analysis and related fields 2006}, SERIES = {Sem. Math. Sci.}, VOLUME = {35}, PAGES = {11--18}, PUBLISHER = {Keio Univ.}, ADDRESS = {Yokohama}, YEAR = {2006}, MRCLASS = {11F20}, MRNUMBER = {MR2331645}, } @article {crtsurvey, AUTHOR = {Beck, Matthias}, TITLE = {Combinatorial reciprocity theorems}, JOURNAL = {Jahresber. Dtsch. Math.-Ver.}, FJOURNAL = {Jahresbericht der Deutschen Mathematiker-Vereinigung}, VOLUME = {114}, YEAR = {2012}, NUMBER = {1}, PAGES = {3--22}, note = {{\tt arXiv:1201.2212}}, ISSN = {0012-0456}, MRCLASS = {05A15 (05C15 05C31 11H06 52C07 52C35)}, MRNUMBER = {2911976}, MRREVIEWER = {David G. Wagner}, DOI = {10.1365/s13291-011-0035-6}, URL = {http://dx.doi.org/10.1365/s13291-011-0035-6}, } @article {shimixedparking, AUTHOR = {Matthias Beck and Ana Berrizbeitia and Michael Dairyko and Claudia Rodriguez and Amanda Ruiz and Schuyler Veenemani}, TITLE = {Parking functions, {S}hi arrangements, and mixed graphs}, JOURNAL = {Amer. Math. Monthly}, FJOURNAL = {The American Mathematical Monthly}, VOLUME = {122}, YEAR = {2015}, PAGES = {660--673}, note = {{\tt arXiv:1405.5587}}, } @article {weakmixed, AUTHOR = {Beck, Matthias and Blado, Daniel and Crawford, Joseph and Jean-Louis, Ta{\"{\i}}na and Young, Michael}, TITLE = {On weak chromatic polynomials of mixed graphs}, JOURNAL = {Graphs Combin.}, FJOURNAL = {Graphs and Combinatorics}, VOLUME = {31}, YEAR = {2015}, NUMBER = {1}, PAGES = {91--98}, note = {{\tt arXiv:1210.4634}}, ISSN = {0911-0119}, MRCLASS = {05C31 (05C15 05C20 06A07)}, MRNUMBER = {3293467}, MRREVIEWER = {Aysel Erey}, DOI = {10.1007/s00373-013-1381-1}, URL = {http://dx.doi.org/10.1007/s00373-013-1381-1}, } @article {symmcones, AUTHOR = {Beck, Matthias and Bliem, Thomas and Braun, Benjamin and Savage, Carla D.}, TITLE = {Lattice point generating functions and symmetric cones}, JOURNAL = {J. Algebraic Combin.}, FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal}, VOLUME = {38}, YEAR = {2013}, NUMBER = {3}, PAGES = {543--566}, note = {{\tt arXiv:1206.1551}}, ISSN = {0925-9899}, MRCLASS = {05A15 (05A17 05E18 11H06)}, MRNUMBER = {3104728}, DOI = {10.1007/s10801-012-0414-9}, URL = {http://dx.doi.org/10.1007/s10801-012-0414-9}, } @article {golomb, AUTHOR = {Beck, Matthias and Bogart, Tristram and Pham, Tu}, TITLE = {Enumeration of {G}olomb rulers and acyclic orientations of mixed graphs}, JOURNAL = {Electron. J. Combin.}, FJOURNAL = {Electronic Journal of Combinatorics}, VOLUME = {19}, YEAR = {2012}, NUMBER = {3}, PAGES = {Paper 42, 13 pp.}, ISSN = {1077-8926}, MRCLASS = {05A15 (05C15 11B75 52B12)}, MRNUMBER = {2988864}, } @article {eulermahonian, AUTHOR = {Beck, Matthias and Braun, Benjamin}, TITLE = {Euler--{M}ahonian statistics via polyhedral geometry}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {244}, YEAR = {2013}, PAGES = {925--954}, note = {{\tt arXiv:1109.3353}}, ISSN = {0001-8708}, MRCLASS = {05A15 (05A05 05A10 05A19 05E15 52B15)}, MRNUMBER = {3077893}, MRREVIEWER = {Edward E. Allen}, DOI = {10.1016/j.aim.2013.06.002}, URL = {http://dx.doi.org/10.1016/j.aim.2013.06.002}, } @article {nowhereharmonic, AUTHOR = {Beck, Matthias and Braun, Benjamin}, TITLE = {Nowhere-harmonic colorings of graphs}, JOURNAL = {Proc. Amer. Math. Soc.}, FJOURNAL = {Proceedings of the American Mathematical Society}, VOLUME = {140}, YEAR = {2012}, NUMBER = {1}, PAGES = {47--63}, note = {{\tt arXiv:0907.1272}}, ISSN = {0002-9939}, CODEN = {PAMYAR}, MRCLASS = {05C15 (05A15 05C30 52B20 52C35)}, MRNUMBER = {2833516 (2012i:05090)}, MRREVIEWER = {David G. Wagner}, DOI = {10.1090/S0002-9939-2011-10879-7}, URL = {http://dx.doi.org/10.1090/S0002-9939-2011-10879-7}, } @article {slecturehall, AUTHOR = {Beck, Matthias and Braun, Benjamin and K{\"o}ppe, Matthias and Savage, Carla D. and Zafeirakopoulos, Zafeirakis}, TITLE = {s-lecture hall partitions, self-reciprocal polynomials, and {G}orenstein cones}, JOURNAL = {Ramanujan J.}, FJOURNAL = {Ramanujan Journal. An International Journal Devoted to the Areas of Mathematics Influenced by Ramanujan}, VOLUME = {36}, YEAR = {2015}, NUMBER = {1-2}, PAGES = {123--147}, note = {{\tt arXiv:1211.0258}}, ISSN = {1382-4090}, MRCLASS = {05A17 (05A19 13H10 52B11)}, DOI = {10.1007/s11139-013-9538-3}, URL = {http://dx.doi.org/10.1007/s11139-013-9538-3}, } MRNUMBER = {3296715}, @Unpublished {slecturehall2, AUTHOR = {Beck, Matthias and Braun, Benjamin and K{\"o}ppe, Matthias and Savage, Carla D. and Zafeirakopoulos, Zafeirakis}, TITLE = {Generating functions and triangulations for lecture hall cones}, note = {Preprint ({\tt arXiv:1508.04619})}, } @incollection {mahonianpartition, AUTHOR = {Beck, Matthias and Braun, Benjamin and Le, Nguyen}, TITLE = {Mahonian partition identities via polyhedral geometry}, BOOKTITLE = {From {F}ourier analysis and number theory to radon transforms and geometry}, SERIES = {Dev. Math.}, VOLUME = {28}, PAGES = {41--54, {\tt arXiv:1103.1070}}, PUBLISHER = {Springer, New York}, YEAR = {2013}, MRCLASS = {05A15 (05A17 11P81 52C07)}, MRNUMBER = {2986952}, MRREVIEWER = {David M. Bressoud}, DOI = {10.1007/978-1-4614-4075-8_3}, URL = {http://dx.doi.org/10.1007/978-1-4614-4075-8_3}, } @article {beckbraunvindasmelendez, AUTHOR = {Beck, Matthias and Braun, Benjamin and Vindas-Mel\'{e}ndez, Andr\'{e}s R.}, TITLE = {Decompositions of {E}hrhart {$h^*$}-{P}olynomials for {R}ational {P}olytopes}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {68}, YEAR = {2022}, NUMBER = {1}, PAGES = {50--71}, ISSN = {0179-5376}, MRCLASS = {52B20 (05A15 05A20 52B11)}, MRNUMBER = {4430280}, DOI = {10.1007/s00454-021-00341-0}, URL = {https://doi.org/10.1007/s00454-021-00341-0}, } @article {cellflows, AUTHOR = {Beck, Matthias and Breuer, Felix and Godkin, Logan and Martin, Jeremy L.}, TITLE = {Enumerating colorings, tensions and flows in cell complexes}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {122}, YEAR = {2014}, PAGES = {82--106}, note = {{\tt arXiv:1212.6539}}, ISSN = {0097-3165}, MRCLASS = {05E45}, MRNUMBER = {3127679}, DOI = {10.1016/j.jcta.2013.10.002}, URL = {http://dx.doi.org/10.1016/j.jcta.2013.10.002}, } @article {beckchavez, AUTHOR = {Beck, Matthias and Chavez, Anastasia}, TITLE = {Bernoulli-{D}edekind sums}, JOURNAL = {Acta Arith.}, FJOURNAL = {Acta Arithmetica}, VOLUME = {149}, YEAR = {2011}, NUMBER = {1}, PAGES = {65--82}, note = {{\tt arXiv:1008.0038}}, ISSN = {0065-1036}, CODEN = {AARIA9}, MRCLASS = {11F20 (11B68)}, MRNUMBER = {2805543}, DOI = {10.4064/aa149-1-5}, URL = {http://0-dx.doi.org.opac.sfsu.edu/10.4064/aa149-1-5}, } @incollection {cottonwood, AUTHOR = {Beck, Matthias and Chen, Beifang and Fukshansky, Lenny and Haase, Christian and Knutson, Allen and Reznick, Bruce and Robins, Sinai and Sch{\"u}rmann, Achill}, TITLE = {Problems from the {C}ottonwood {R}oom}, BOOKTITLE = {Integer {P}oints in {P}olyhedra---{G}eometry, {N}umber {T}heory, {A}lgebra, {O}ptimization}, SERIES = {Contemp. Math.}, VOLUME = {374}, PAGES = {179--191}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {2005}, MRCLASS = {11-02}, MRNUMBER = {MR2134767}, } @article {magic, AUTHOR = {Beck, Matthias and Cohen, Moshe and Cuomo, Jessica and Gribelyuk, Paul}, TITLE = {The number of ``magic'' squares, cubes, and hypercubes}, JOURNAL = {Amer. Math. Monthly}, FJOURNAL = {The American Mathematical Monthly}, VOLUME = {110}, YEAR = {2003}, NUMBER = {8}, PAGES = {707--717}, note = {{\tt arXiv:math.CO/0201013}}, ISSN = {0002-9890}, CODEN = {AMMYAE}, MRCLASS = {05A15 (52B20)}, MRNUMBER = {2 023 999}, MRREVIEWER = {David Perkinson}, } @article {vectorflows, AUTHOR = {Beck, Matthias and Cuyjet, Alyssa and Kirby, Gordon Rojas and Stubblefield, Molly and Young, Michael}, TITLE = {Nowhere-zero {$\vec{k}$}-flows on graphs}, JOURNAL = {Ann. Comb.}, FJOURNAL = {Annals of Combinatorics}, VOLUME = {18}, YEAR = {2014}, NUMBER = {4}, PAGES = {579--583}, note = {{\tt arXiv:1305.2456}}, ISSN = {0218-0006}, MRCLASS = {05C21 (05A15 05C31)}, MRNUMBER = {3282647}, DOI = {10.1007/s00026-014-0246-5}, URL = {http://dx.doi.org/10.1007/s00026-014-0246-5}, } @article {veryample, AUTHOR = {Beck, Matthias and Delgado, Jessica and Gubeladze, Joseph and Michalek, Mateusz}, TITLE = {Very ample and {K}oszul segmental fibers}, JOURNAL = {J. Algebraic Combin.}, FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal}, VOLUME = {42}, YEAR = {2015}, PAGES = {165--182}, note = {{\tt arXiv:1307.7422}}, } @incollection {coeffzeros, AUTHOR = {Beck, Matthias and De Loera, Jes{\'u}s A. and Develin, Mike and Pfeifle, Julian and Stanley, Richard P.}, TITLE = {Coefficients and roots of {E}hrhart polynomials}, BOOKTITLE = {Integer {P}oints in {P}olyhedra---{G}eometry, {N}umber {T}heory, {A}lgebra, {O}ptimization}, SERIES = {Contemp. Math.}, VOLUME = {374}, PAGES = {15--36, {\tt arXiv:math.CO/0402148}}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {2005}, MRCLASS = {52C07 (05A15 52B20)}, MRNUMBER = {MR2134759}, } @article {intervalvector, AUTHOR = {Beck, Matthias and De Silva, Jessica and Dorfsman--Hopkins, Gabriel and Pruitt, Joseph and Ruiz, Amanda}, TITLE = {The combinatorics of interval-vector polytopes}, JOURNAL = {Electron. J. Combin.}, FJOURNAL = {Electronic Journal of Combinatorics}, VOLUME = {20}, YEAR = {2013}, NUMBER = {3}, PAGES = {Paper 22, 12 pp.}, ISSN = {1077-8926}, MRCLASS = {52B12 (05A15 52B05)}, MRNUMBER = {3104520}, MRREVIEWER = {Ruriko Yoshida}, } @article {gorenstein, AUTHOR = {Beck, Matthias and Jayawant, Pallavi and McAllister, Tyrrell B.}, TITLE = {Lattice-point generating functions for free sums of convex sets}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {120}, YEAR = {2013}, NUMBER = {6}, PAGES = {1246--1262}, note = {{\tt arXiv:1207.0164}}, ISSN = {0097-3165}, MRCLASS = {52C07 (05A15)}, MRNUMBER = {3044541}, MRREVIEWER = {Benjamin Braun}, DOI = {10.1016/j.jcta.2013.03.007}, URL = {http://dx.doi.org/10.1016/j.jcta.2013.03.007}, } @incollection {simpflows, AUTHOR = {Beck, Matthias and Kemper, Yvonne}, TITLE = {Flows on simplicial complexes}, 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., AR}, PAGES = {817--826, {\tt arXiv:1206.2260}}, PUBLISHER = {Assoc. Discrete Math. Theor. Comput. Sci., Nancy}, YEAR = {2012}, MRCLASS = {05E45}, MRNUMBER = {2958051}, } @article {bdr, AUTHOR = {Beck, Matthias and Diaz, Ricardo and Robins, Sinai}, TITLE = {The {F}robenius problem, rational polytopes, and {F}ourier-{D}edekind sums}, JOURNAL = {J. Number Theory}, FJOURNAL = {Journal of Number Theory}, VOLUME = {96}, YEAR = {2002}, NUMBER = {1}, PAGES = {1--21}, note = {{\tt arXiv:math.NT/0204035}}, ISSN = {0022-314X}, CODEN = {JNUTA9}, MRCLASS = {11P21 (11D04 11F20)}, MRNUMBER = {2003j:11117}, MRREVIEWER = {Ira Gessel}, } @article {frobcomp, AUTHOR = {Beck, Matthias and Einstein, David and Zacks, Shelemyahu}, TITLE = {Some experimental results on the {F}robenius problem}, JOURNAL = {Experiment. Math.}, FJOURNAL = {Experimental Mathematics}, VOLUME = {12}, YEAR = {2003}, NUMBER = {3}, PAGES = {263--269}, note = {{\tt arXiv:math.NT/0204036}}, ISSN = {1058-6458}, MRCLASS = {11D04}, MRNUMBER = {2 034 391}, } @article {Beckbop, AUTHOR = {Beck, Matthias and Farahmand, Maryam and Karunaratne, Gina and Zuniga Ruiz, Sandra}, TITLE = {Bivariate order polynomials}, JOURNAL = {Graphs Combin.}, FJOURNAL = {Graphs and Combinatorics}, VOLUME = {36}, YEAR = {2020}, NUMBER = {4}, PAGES = {921--931}, ISSN = {0911-0119}, DOI = {10.1007/s00373-019-02128-w}, URL = {https://doi.org/10.1007/s00373-019-02128-w}, } @article {frobpol, AUTHOR = {Beck, Matthias and Gessel, Ira M. and Komatsu, Takao}, TITLE = {The polynomial part of a restricted partition function related to the {F}robenius problem}, JOURNAL = {Electron. J. Combin.}, FJOURNAL = {Electronic Journal of Combinatorics}, VOLUME = {8}, YEAR = {2001}, NUMBER = {1}, PAGES = {Note 7, 5 pp.}, ISSN = {1077-8926}, MRCLASS = {05A17 (11P82)}, MRNUMBER = {2002f:05017}, MRREVIEWER = {Jiang Zeng}, } @article{beckgesselleesavage, AUTHOR = {Beck, Matthias and Gessel, Ira M. and Lee, Sunyoung and Savage, Carla D.}, TITLE = {Symmetrically constrained compositions}, JOURNAL = {Ramanujan J.}, FJOURNAL = {Ramanujan Journal. An International Journal Devoted to the Areas of Mathematics Influenced by Ramanujan}, VOLUME = {23}, YEAR = {2010}, NUMBER = {1-3}, PAGES = {355--369}, note = {{\tt arXiv:0906.5573}}, ISSN = {1382-4090}, CODEN = {RAJOF9}, MRCLASS = {11P81 (05A15 05A17 11P21)}, MRNUMBER = {2739223}, MRREVIEWER = {L{\'a}szl{\'o} Lipt{\'a}k}, DOI = {10.1007/s11139-010-9232-7}, URL = {http://0-dx.doi.org.opac.sfsu.edu/10.1007/s11139-010-9232-7}, } @article {bhm, AUTHOR = {Beck, Matthias and Haase, Christian and Matthews, Asia R.}, TITLE = {Dedekind--{C}arlitz polynomials as lattice-point enumerators in rational polyhedra}, JOURNAL = {Math. Ann.}, FJOURNAL = {Mathematische Annalen}, VOLUME = {341}, YEAR = {2008}, NUMBER = {4}, PAGES = {945--961}, note = {{\tt arXiv:0710.1323}}, ISSN = {0025-5831}, CODEN = {MAANA}, MRCLASS = {11P21 (11F20)}, MRNUMBER = {MR2407333 (2009k:11161)}, DOI = {10.1007/s00208-008-0220-9}, URL = {http://0-dx.doi.org.opac.sfsu.edu/10.1007/s00208-008-0220-9}, } @article {gridgraphs, AUTHOR = {Beck, Matthias and Haase, Christian and Sam, Steven V}, TITLE = {Grid graphs, {G}orenstein polytopes, and domino stackings}, JOURNAL = {Graphs Combin.}, FJOURNAL = {Graphs and Combinatorics}, VOLUME = {25}, YEAR = {2009}, NUMBER = {4}, PAGES = {409--426}, note = {{\tt arXiv:0711.4151}}, ISSN = {0911-0119}, CODEN = {GRCOE5}, MRCLASS = {52B20 (05B50 05C70 52C07)}, MRNUMBER = {2575592 (2011b:52013)}, MRREVIEWER = {Alexander I. Barvinok}, DOI = {10.1007/s00373-005-0858-y}, URL = {http://0-dx.doi.org.opac.sfsu.edu/10.1007/s00373-005-0858-y}, } @article {brionlawrence, AUTHOR = {Beck, Matthias and Haase, Christian and Sottile, Frank}, TITLE = {Formulas of {B}rion, {L}awrence, and {V}archenko on rational generating functions for cones}, JOURNAL = {Math. Intelligencer}, FJOURNAL = {The Mathematical Intelligencer}, VOLUME = {31}, YEAR = {2009}, NUMBER = {1}, PAGES = {9--17}, note = {{\tt arXiv:math.CO/0506466}}, ISSN = {0343-6993}, CODEN = {MAINDC}, MRCLASS = {52C05 (05A15)}, MRNUMBER = {MR2480796}, } @article {beckhalloran, AUTHOR = {Beck, Matthias and Halloran, Mary}, TITLE = {Finite trigonometric character sums via discrete {F}ourier analysis}, JOURNAL = {Int. J. Number Theory}, FJOURNAL = {International Journal of Number Theory}, VOLUME = {6}, YEAR = {2010}, NUMBER = {1}, PAGES = {51--67}, note = {{\tt arXiv:0804.0645}}, ISSN = {1793-0421}, MRCLASS = {11L03 (11E41 11R11 11R29)}, MRNUMBER = {2641714 (2011d:11192)}, MRREVIEWER = {Marvin I. Knopp}, DOI = {10.1142/S1793042110002806}, URL = {http://0-dx.doi.org.opac.sfsu.edu/10.1142/S1793042110002806}, } @article {bichromatic, AUTHOR = {Beck, Matthias and Hardin, Mela}, TITLE = {A bivariate chromatic polynomial for signed graphs}, JOURNAL = {Graphs Combin.}, FJOURNAL = {Graphs and Combinatorics}, VOLUME = {31}, YEAR = {2015}, NUMBER = {5}, PAGES = {1211--1221}, note = {{\tt arXiv:1204.2568}}, ISSN = {0911-0119}, MRCLASS = {05C15 (05A15 05C22 05C31 11P21)}, MRNUMBER = {3386004}, MRREVIEWER = {Naduvath K. Sudev}, DOI = {10.1007/s00373-014-1481-6}, URL = {https://doi.org/10.1007/s00373-014-1481-6}, } @article {beckhosten, AUTHOR = {Beck, Matthias and Ho{\c{s}}ten, Serkan}, TITLE = {Cyclotomic polytopes and growth series of cyclotomic lattices}, JOURNAL = {Math. Res. Lett.}, FJOURNAL = {Mathematical Research Letters}, VOLUME = {13}, YEAR = {2006}, NUMBER = {4}, PAGES = {607--622}, ISSN = {1073-2780}, MRCLASS = {11H06 (52B20 52C07)}, MRNUMBER = {MR2250495}, } @article {frobextreme, AUTHOR = {Beck, Matthias and Kifer, Curtis}, TITLE = {An extreme family of generalized {F}robenius numbers}, JOURNAL = {Integers}, FJOURNAL = {Integers. Electronic Journal of Combinatorial Number Theory}, VOLUME = {11}, YEAR = {2011}, PAGES = {Paper A24, 6 pp.}, ISSN = {1867-0652}, MRCLASS = {11D07}, MRNUMBER = {2798635}, } @article {beckpixton, AUTHOR = {Beck, Matthias and Pixton, Dennis}, TITLE = {The {E}hrhart polynomial of the {B}irkhoff polytope}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {30}, YEAR = {2003}, NUMBER = {4}, PAGES = {623--637}, note = {{\tt arXiv:math.CO/0202267}}, ISSN = {0179-5376}, CODEN = {DCGEER}, MRCLASS = {05A15 (52Bxx)}, MRNUMBER = {2 013 976}, } @article {comparithm, AUTHOR = {Beck, Matthias and Robbins, Neville}, TITLE = {Variations on a generating-function theme: enumerating compositions with parts avoiding an arithmetic sequence}, JOURNAL = {Amer. Math. Monthly}, FJOURNAL = {American Mathematical Monthly}, VOLUME = {122}, YEAR = {2015}, NUMBER = {3}, PAGES = {256--263}, note = {{\tt arXiv:1403.0665}}, ISSN = {0002-9890}, MRCLASS = {11P83 (05A17)}, MRNUMBER = {3327715}, DOI = {10.4169/amer.math.monthly.122.03.256}, URL = {http://dx.doi.org/10.4169/amer.math.monthly.122.03.256}, } @article {polygons, AUTHOR = {Beck, Matthias and Robins, Sinai}, TITLE = {Explicit and efficient formulas for the lattice point count in rational polygons using {D}edekind--{R}ademacher sums}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {27}, YEAR = {2002}, NUMBER = {4}, PAGES = {443--459}, note = {{\tt arXiv:math.CO/0111329}}, ISSN = {0179-5376}, CODEN = {DCGEER}, MRCLASS = {11P21 (52Cxx)}, MRNUMBER = {1 902 672}, } @incollection {frobnote, AUTHOR = {Beck, Matthias and Robins, Sinai}, TITLE = {A formula related to the {F}robenius problem in two dimensions}, BOOKTITLE = {Number theory (New York, 2003)}, PAGES = {17--23, {\tt arXiv:math.NT/0204037}}, PUBLISHER = {Springer}, ADDRESS = {New York}, YEAR = {2004}, MRCLASS = {11D04 (11P21)}, MRNUMBER = {2 044 510}, } @incollection {beckrobinsdedekind, AUTHOR = {Beck, Matthias and Robins, Sinai}, TITLE = {Dedekind sums: a combinatorial-geometric viewpoint}, BOOKTITLE = {Unusual applications of number theory}, SERIES = {DIMACS Ser. Discrete Math. Theoret. Comput. Sci.}, VOLUME = {64}, PAGES = {25--35, {\tt arXiv:math.NT/0112076}}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {2004}, MRCLASS = {11F20 (05A15 11L03)}, MRNUMBER = {2 063 199}, } @book{ccd, AUTHOR = {Beck, Matthias and Robins, Sinai}, TITLE = {Computing the {C}ontinuous {D}iscretely: Integer-point {E}numeration in {P}olyhedra}, SERIES = {Undergraduate Texts in Mathematics}, EDITION = {Second}, 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)}, DOI = {10.1007/978-1-4939-2969-6}, URL = {http://dx.doi.org/10.1007/978-1-4939-2969-6}, } @article {solidangle, AUTHOR = {Beck, Matthias and Robins, Sinai and Sam, Steven V}, TITLE = {Positivity theorems for solid-angle polynomials}, JOURNAL = {Beitr\"age Algebra Geom.}, FJOURNAL = {Beitr\"age zur Algebra und Geometrie. Contributions to Algebra and Geometry}, VOLUME = {51}, YEAR = {2010}, NUMBER = {2}, PAGES = {493--507}, note = {{\tt arXiv:0906.4031}; Corrigendum in Beiträge zur Algebra und Geometrie 56, no. 2 (2015), 775–776}, ISSN = {0138-4821}, MRCLASS = {28A75 (05A15 52C07)}, MRNUMBER = {2663951 (2011e:28005)}, } @article {maxperiods, AUTHOR = {Beck, Matthias and Sam, Steven V and Woods, Kevin M.}, TITLE = {Maximal periods of ({E}hrhart) quasi-polynomials}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {115}, YEAR = {2008}, NUMBER = {3}, PAGES = {517--525}, note = {{\tt arXiv:math/0702242}}, ISSN = {0097-3165}, CODEN = {JCBTA7}, MRCLASS = {05A15 (52B11 52C07)}, MRNUMBER = {2402608 (2009c:05006)}, MRREVIEWER = {Alan Stapledon}, DOI = {10.1016/j.jcta.2007.05.009}, URL = {http://0-dx.doi.org.opac.sfsu.edu/10.1016/j.jcta.2007.05.009}, } @article {bsstanleyirrational, AUTHOR = {Beck, Matthias and Sottile, Frank}, TITLE = {Irrational proofs for three theorems of {S}tanley}, JOURNAL = {European J. Combin.}, FJOURNAL = {European Journal of Combinatorics}, VOLUME = {28}, YEAR = {2007}, NUMBER = {1}, PAGES = {403--409}, note = {{\tt arXiv:math.CO/0506315}}, ISSN = {0195-6698}, MRCLASS = {52B11 (05A15 52C07)}, MRNUMBER = {MR2261827 (2007f:52029)}, MRREVIEWER = {Robin Chapman}, } @article {beckstapledon, AUTHOR = {Beck, Matthias and Stapledon, Alan}, TITLE = {On the log-concavity of {H}ilbert series of {V}eronese subrings and {E}hrhart series}, JOURNAL = {Math. 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Y.}, TITLE = {The relation connecting the angle-sums and volume of a polytope in space of $n$ dimensions}, JOURNAL = {Proc. Roy. Soc. London, Ser. A}, VOLUME = {115}, YEAR = {1927}, PAGES = {103--119}, } @article {sotskovtanaev, AUTHOR = {Sotskov, Ju. N. and Tanaev, V. S.}, TITLE = {Chromatic polynomial of a mixed graph}, JOURNAL = {Vesc\=\i\ Akad. Navuk BSSR Ser. F\=\i z.-Mat. Navuk}, FJOURNAL = {Vesc\=\i\ Akad\`em\=\i \=\i\ Navuk BSSR. Seryja F\=\i z\=\i ka-Mat\`ematy\v cnyh Navuk}, YEAR = {1976}, NUMBER = {6}, PAGES = {20--23, 140}, ISSN = {0002-3574}, MRCLASS = {05C15}, MRNUMBER = {0463008 (57 \#2972)}, MRREVIEWER = {D. Cvetkovic}, } @article {SoTaWe, AUTHOR = {Sotskov, Yuri N. and Tanaev, Vjacheslav S. and Werner, Frank}, TITLE = {Scheduling problems and mixed graph colorings}, JOURNAL = {Optimization}, FJOURNAL = {Optimization. A Journal of Mathematical Programming and Operations Research}, VOLUME = {51}, YEAR = {2002}, NUMBER = {3}, PAGES = {597--624}, ISSN = {0233-1934}, MRCLASS = {90B35 (05C15)}, MRNUMBER = {1927912 (2003g:90024)}, MRREVIEWER = {Mechthild Opperud}, DOI = {10.1080/0233193021000004994}, URL = {http://0-dx.doi.org.opac.sfsu.edu/10.1080/0233193021000004994}, } @article {spencermagic, AUTHOR = {Spencer, Joel}, TITLE = {Counting magic squares}, JOURNAL = {Amer. Math. Monthly}, FJOURNAL = {The American Mathematical Monthly}, VOLUME = {87}, YEAR = {1980}, NUMBER = {5}, PAGES = {397--399}, ISSN = {0002-9890}, CODEN = {AMMYAE}, MRCLASS = {05B30 (05A15)}, MRNUMBER = {81j:05042}, MRREVIEWER = {H. Gupta}, } @article {sperner, AUTHOR = {Sperner, E.}, TITLE = {Ein {S}atz \"uber {U}ntermengen einer endlichen {M}enge}, JOURNAL = {Math.~Z.}, VOLUME = {27}, YEAR = {1928}, PAGES = {544--548}, } @book {spiegelodonnell, AUTHOR = {Spiegel, Eugene and O'Donnell, Christopher J.}, TITLE = {Incidence algebras}, SERIES = {Monographs and Textbooks in Pure and Applied Mathematics}, VOLUME = {206}, PUBLISHER = {Marcel Dekker Inc.}, ADDRESS = {New York}, YEAR = {1997}, PAGES = {x+335}, ISBN = {0-8247-0036-8}, MRCLASS = {06-02 (05-02 16S99)}, MRNUMBER = {1445562 (98g:06001)}, MRREVIEWER = {Giovanni Ferrero}, } @article {Sprea, AUTHOR = {Spreafico, Mauro}, TITLE = {On the {B}arnes double zeta and {G}amma functions}, JOURNAL = {J. Number Theory}, FJOURNAL = {Journal of Number Theory}, VOLUME = {129}, YEAR = {2009}, NUMBER = {9}, PAGES = {2035--2063}, ISSN = {0022-314X}, CODEN = {JNUTA9}, MRCLASS = {11M41 (11M32 33B15)}, MRNUMBER = {2528052 (2010h:11149)}, MRREVIEWER = {Matilde N. Lal{\'{\i}}n}, DOI = {10.1016/j.jnt.2009.03.005}, URL = {http://dx.doi.org/10.1016/j.jnt.2009.03.005}, } @incollection {stanleyzonotopegraphicaldegree, AUTHOR = {Stanley, Richard P.}, TITLE = {A zonotope associated with graphical degree sequences}, BOOKTITLE = {Applied geometry and discrete mathematics}, SERIES = {DIMACS Ser. Discrete Math. Theoret. Comput. Sci.}, VOLUME = {4}, PAGES = {555--570}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {1991}, MRCLASS = {52B20 (05C30 52B05)}, MRNUMBER = {1116376 (92k:52020)}, MRREVIEWER = {P. McMullen}, } @article {stanleyhowupperbound, AUTHOR = {Stanley, Richard P.}, TITLE = {How the {U}pper {B}ound {C}onjecture {W}as {P}roved}, JOURNAL = {Ann. Comb.}, FJOURNAL = {Annals of Combinatorics}, VOLUME = {18}, YEAR = {2014}, NUMBER = {3}, PAGES = {533--539}, ISSN = {0218-0006}, MRNUMBER = {3245897}, DOI = {10.1007/s00026-014-0238-5}, URL = {http://dx.doi.org/10.1007/s00026-014-0238-5}, } @incollection {stanleychromaticlike, AUTHOR = {Stanley, Richard P.}, TITLE = {A chromatic-like polynomial for ordered sets}, BOOKTITLE = {Proc. {S}econd {C}hapel {H}ill {C}onf. on {C}ombinatorial {M}athematics and its {A}pplications ({U}niv. {N}orth {C}arolina, {C}hapel {H}ill, {N}.{C}., 1970)}, PAGES = {421--427}, PUBLISHER = {Univ. North Carolina, Chapel Hill, N.C.}, YEAR = {1970}, MRCLASS = {05.55}, MRNUMBER = {0269545}, MRREVIEWER = {W. T. Tutte}, } @article {stanleydecomp, 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}, QUIETMRNUMBER = {82a:52007}, MRREVIEWER = {P. McMullen}, } @article {stanleyshiproceedings, AUTHOR = {Stanley, Richard P.}, TITLE = {Hyperplane arrangements, interval orders, and trees}, JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.}, FJOURNAL = {Proceedings of the National Academy of Sciences of the United States of America}, VOLUME = {93}, YEAR = {1996}, NUMBER = {6}, PAGES = {2620--2625}, ISSN = {0027-8424}, CODEN = {PNASA6}, MRCLASS = {52B30 (05C30 06A06 20F55)}, MRNUMBER = {1379568 (97i:52013)}, MRREVIEWER = {Hiroaki Terao}, DOI = {10.1073/pnas.93.6.2620}, URL = {http://0-dx.doi.org.opac.sfsu.edu/10.1073/pnas.93.6.2620}, } @book{stanleycatalan, AUTHOR = {Stanley, Richard P.}, TITLE = {Catalan {N}umbers}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, YEAR = {2015}, } @book{stanleyec1, AUTHOR = {Stanley, Richard P.}, TITLE = {Enumerative {C}ombinatorics. {V}olume 1}, SERIES = {Cambridge Studies in Advanced Mathematics}, VOLUME = {49}, EDITION = {Second}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, YEAR = {2012}, PAGES = {xiv+626}, ISBN = {978-1-107-60262-5}, MRCLASS = {05-02 (05A15 06-02)}, MRNUMBER = {2868112}, } @book {stanleyec2, AUTHOR = {Stanley, Richard P.}, TITLE = {Enumerative {C}ombinatorics. {V}olume 2}, SERIES = {Cambridge Studies in Advanced Mathematics}, VOLUME = {62}, NOTE = {With a foreword by Gian--Carlo Rota and appendix 1 by Sergey Fomin}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, YEAR = {1999}, PAGES = {xii+581}, ISBN = {0-521-56069-1; 0-521-78987-7}, MRCLASS = {05A15 (05-02 05E05 05E10 68R05)}, MRNUMBER = {2000k:05026}, MRREVIEWER = {Ira Gessel}, } @book {stanleycombcommalg, AUTHOR = {Stanley, Richard P.}, TITLE = {Combinatorics and {C}ommutative {A}lgebra}, SERIES = {Progress in Mathematics}, VOLUME = {41}, EDITION = {Second}, PUBLISHER = {Birkh\"auser Boston Inc.}, ADDRESS = {Boston, MA}, YEAR = {1996}, PAGES = {x+164}, ISBN = {0-8176-3836-9}, MRCLASS = {05-02 (13F50)}, MRNUMBER = {98h:05001}, MRREVIEWER = {Volkmar Welker}, } @article {stanleyacyclic, AUTHOR = {Stanley, Richard P.}, TITLE = {Acyclic orientations of graphs}, JOURNAL = {Discrete Math.}, VOLUME = {5}, YEAR = {1973}, PAGES = {171--178}, MRCLASS = {05C20 (05C15 06A10)}, MRNUMBER = {47 \#6537}, MRREVIEWER = {R. C. Read}, } @article {stanleymagic, AUTHOR = {Stanley, Richard P.}, TITLE = {Linear homogeneous {D}iophantine equations and magic labelings of graphs}, JOURNAL = {Duke Math. J.}, VOLUME = {40}, YEAR = {1973}, PAGES = {607--632}, MRCLASS = {05B30}, MRNUMBER = {47 \#6519}, MRREVIEWER = {H. Gupta}, } @article {stanleymagiccohenmac, AUTHOR = {Stanley, Richard P.}, TITLE = {Magic labelings of graphs, symmetric magic squares, systems of parameters, and {C}ohen--{M}acaulay rings}, JOURNAL = {Duke Math. J.}, FJOURNAL = {Duke Mathematical Journal}, VOLUME = {43}, YEAR = {1976}, NUMBER = {3}, PAGES = {511--531}, ISSN = {0012-7094}, MRCLASS = {05C30 (13H10)}, MRNUMBER = {0444514 (56 \#2865)}, MRREVIEWER = {S. G. Hoggar}, } @article {stanleyupperbound, AUTHOR = {Stanley, Richard P.}, TITLE = {The upper bound conjecture and {C}ohen--{M}acaulay rings}, JOURNAL = {Studies in Appl. Math.}, VOLUME = {54}, YEAR = {1975}, NUMBER = {2}, PAGES = {135--142}, MRCLASS = {57C15 (13H10 52A25)}, MRNUMBER = {0458437 (56 \#16640)}, MRREVIEWER = {P. McMullen}, } @article {staneleygroupsonposets, AUTHOR = {Stanley, Richard P.}, TITLE = {Some aspects of groups acting on finite posets}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {32}, YEAR = {1982}, NUMBER = {2}, PAGES = {132--161}, ISSN = {0097-3165}, CODEN = {JCBTA7}, MRCLASS = {06A10 (14L30 20B25)}, MRNUMBER = {654618 (83d:06002)}, MRREVIEWER = {R. J. Bumcrot}, DOI = {10.1016/0097-3165(82)90017-6}, URL = {http://dx.doi.org/10.1016/0097-3165(82)90017-6}, } @article {stanleyreciprocity, AUTHOR = {Stanley, Richard P.}, TITLE = {Combinatorial reciprocity theorems}, JOURNAL = {Advances in Math.}, VOLUME = {14}, YEAR = {1974}, PAGES = {194--253}, MRCLASS = {05A15 (10E05)}, MRNUMBER = {54 \#111}, MRREVIEWER = {G. L. Alexanderson}, } @article {stanleyposetpolytopes, 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}, ISSN = {0179-5376}, CODEN = {DCGEER}, MRCLASS = {52A25 (52A40)}, MRNUMBER = {87e:52012}, MRREVIEWER = {P. McMullen}, } @incollection {stanleyhyparr, AUTHOR = {Stanley, Richard P.}, TITLE = {An introduction to hyperplane arrangements}, BOOKTITLE = {Geometric combinatorics}, SERIES = {IAS/Park City Math. Ser.}, VOLUME = {13}, PAGES = {389--496}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {2007}, MRCLASS = {52C35 (05B35 55R80)}, MRNUMBER = {MR2383131}, } @article {stanleymonotonicity, AUTHOR = {Stanley, Richard P.}, TITLE = {A monotonicity property of {$h$}-vectors and {$h^*$}-vectors}, JOURNAL = {European J. Combin.}, FJOURNAL = {European Journal of Combinatorics}, VOLUME = {14}, YEAR = {1993}, NUMBER = {3}, PAGES = {251--258}, ISSN = {0195-6698}, MRCLASS = {52B20 (05E99 06A07 06A08 13F50)}, MRNUMBER = {1215335 (94f:52016)}, DOI = {10.1006/eujc.1993.1028}, URL = {http://0-dx.doi.org.opac.sfsu.edu/10.1006/eujc.1993.1028}, } @book {stanleythesis, AUTHOR = {Stanley, Richard P.}, TITLE = {Ordered structures and partitions}, NOTE = {Memoirs of the American Mathematical Society, No. 119}, PUBLISHER = {American Mathematical Society}, ADDRESS = {Providence, R.I.}, YEAR = {1972}, PAGES = {iii+104}, MRCLASS = {05A17}, MRNUMBER = {0332509 (48 \#10836)}, MRREVIEWER = {L. K. Durst}, } @article {stanleyhilbertgradedalgebras, AUTHOR = {Stanley, Richard P.}, TITLE = {Hilbert functions of graded algebras}, JOURNAL = {Advances in Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {28}, YEAR = {1978}, NUMBER = {1}, PAGES = {57--83}, ISSN = {0001-8708}, MRCLASS = {13D10 (13H10)}, MRNUMBER = {0485835 (58 \#5637)}, MRREVIEWER = {Idun Reiten}, } @article {stanleyinequ, AUTHOR = {Stanley, Richard P.}, TITLE = {On the {H}ilbert function of a graded {C}ohen--{M}acaulay domain}, JOURNAL = {J. Pure Appl. Algebra}, FJOURNAL = {Journal of Pure and Applied Algebra}, VOLUME = {73}, YEAR = {1991}, NUMBER = {3}, PAGES = {307--314}, ISSN = {0022-4049}, CODEN = {JPAAA2}, MRCLASS = {13D40 (13A02 13H10 52B20)}, MRNUMBER = {1124790 (92f:13017)}, MRREVIEWER = {Matthew Miller}, DOI = {10.1016/0022-4049(91)90034-Y}, URL = {http://dx.doi.org/10.1016/0022-4049(91)90034-Y}, } @incollection {stanleyparkcityhyperplanes, AUTHOR = {Stanley, Richard P.}, TITLE = {An introduction to hyperplane arrangements}, BOOKTITLE = {Geometric combinatorics}, SERIES = {IAS/Park City Math. Ser.}, VOLUME = {13}, PAGES = {389--496}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {2007}, MRCLASS = {52C35 (05B35 55R80)}, MRNUMBER = {2383131}, } @article {stanleycohenmacauleydomain, AUTHOR = {Stanley, Richard P.}, TITLE = {On the {H}ilbert function of a graded {C}ohen-{M}acaulay domain}, JOURNAL = {J. Pure Appl. Algebra}, FJOURNAL = {Journal of Pure and Applied Algebra}, VOLUME = {73}, YEAR = {1991}, NUMBER = {3}, PAGES = {307--314}, ISSN = {0022-4049}, CODEN = {JPAAA2}, MRCLASS = {13D40 (13A02 13H10 52B20)}, MRNUMBER = {1124790 (92f:13017)}, MRREVIEWER = {Matthew Miller}, DOI = {10.1016/0022-4049(91)90034-Y}, URL = {http://0-dx.doi.org.opac.sfsu.edu/10.1016/0022-4049(91)90034-Y}, } @incollection {stanleylogconcave, AUTHOR = {Stanley, Richard P.}, TITLE = {Log-concave and unimodal sequences in algebra, combinatorics, and geometry}, BOOKTITLE = {Graph theory and its applications: {E}ast and {W}est ({J}inan, 1986)}, SERIES = {Ann. New York Acad. Sci.}, VOLUME = {576}, PAGES = {500--535}, PUBLISHER = {New York Acad. Sci., New York}, YEAR = {1989}, MRCLASS = {05E15 (05E10 20C15 52B20)}, MRNUMBER = {1110850 (92e:05124)}, MRREVIEWER = {L. Bruce Richmond}, DOI = {10.1111/j.1749-6632.1989.tb16434.x}, URL = {http://dx.doi.org/10.1111/j.1749-6632.1989.tb16434.x}, } @article {stanleylocalhvectors, AUTHOR = {Stanley, Richard P.}, TITLE = {Subdivisions and local {$h$}-vectors}, JOURNAL = {J. Amer. Math. Soc.}, FJOURNAL = {Journal of the American Mathematical Society}, VOLUME = {5}, YEAR = {1992}, NUMBER = {4}, PAGES = {805--851}, ISSN = {0894-0347}, MRCLASS = {52B20 (05E99 06A07 13D40 55U10)}, MRNUMBER = {1157293 (93b:52012)}, MRREVIEWER = {Margaret M. Bayer}, DOI = {10.2307/2152711}, URL = {http://dx.doi.org/10.2307/2152711}, } @article {stapledonweightedehrart, AUTHOR = {Stapledon, Alan}, TITLE = {Weighted {E}hrhart theory and orbifold cohomology}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {219}, YEAR = {2008}, NUMBER = {1}, PAGES = {63--88}, ISSN = {0001-8708}, CODEN = {ADMTA4}, MRCLASS = {14M25 (14F43 52B05)}, MRNUMBER = {2435420 (2009i:14074)}, MRREVIEWER = {J. Maurice Rojas}, DOI = {10.1016/j.aim.2008.04.010}, URL = {http://dx.doi.org/10.1016/j.aim.2008.04.010}, } @article {stapledondelta, AUTHOR = {Stapledon, Alan}, TITLE = {Inequalities and {E}hrhart {$\delta$}-vectors}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {361}, YEAR = {2009}, NUMBER = {10}, PAGES = {5615--5626}, ISSN = {0002-9947}, CODEN = {TAMTAM}, MRCLASS = {52B20}, MRNUMBER = {2515826 (2010e:52026)}, MRREVIEWER = {Benjamin Braun}, DOI = {10.1090/S0002-9947-09-04776-X}, URL = {http://dx.doi.org/10.1090/S0002-9947-09-04776-X}, } @Unpublished{alfonsin, title = {The diophantine {F}robenius problem}, author = {Ram{\'{\i}}rez Alfons{\'{\i}}n, Jorge L.}, note = {Report No.~00893, Forschungsinstitut f\"ur diskrete Mathematik, Universit\"at Bonn}, year = 2000 } @Unpublished{mudgal, title = {Counting Magic Squares}, author = {Mudgal, Apurva}, note = {Undergraduate thesis, IIT Bombay}, year = 2002 } @Unpublished {gordonfrob, AUTHOR = {Gordon, Basil}, TITLE = {Piecewise Linear Recurrences}, note = {to appear}, } @Unpublished{conicdecomp, author = {Matthias Beck and Sinai Robins and Frank Sottile and Jonathan Weitsman}, title = {Conic decompositions of polytopes}, note = {Preprint}, year = {2003} } @Unpublished{baldonivergne, title = {{Residue formulae for volumes and {E}hrhart polynomials of convex polytopes}}, author = {Velleda Baldoni and Mich\`ele Vergne}, note = {Preprint ({\tt arXiv:math.CO/0103097})}, } @Unpublished{bwz, author = {Matthias Beck and Xueqin Wang and Thomas Zaslavsky}, title = {A unifying generalization of {S}perner's theorem}, note = {Preprint ({\tt arXiv:math.CO/0112067})}, year = {2003} } @Unpublished{dedprob, author = {Matthias Beck and Sinai Robins and Shelemyahu Zacks}, title = {Higher-dimensional {D}edekind sums and their bounds arising from the discrete diagonal of the $n$-cube}, note = {Preprint ({\tt arXiv:math.NT/0305421}), to appear in \emph{Adv. Appl. Math.}}, year = {2005} } @Unpublished{ehrhartextended, author = {Matthias Beck and Richard Ehrenborg}, title = {Ehrhart--{M}acdonald reciprocity extended}, note = {Preprint ({\tt arXiv:math.CO/0504230})}, } @Unpublished {patrassole, AUTHOR = {Patras, Fr\'ed\'eric and Sol\'e, Patrick}, TITLE = {The coordinator polynomial of some cyclotomic lattices}, note = {Preprint, to appear in European J. Combin.}, year = 2006 } @Unpublished {ramirezhilbert, author = {Ram{\'{\i}}rez Alfons{\'{\i}}n, Jorge L.}, TITLE = {The {F}robenius number via {H}ilbert series}, note = {Preprint}, year = {2002}, } @Unpublished {einsteinlichtblaustrzebonskiwagon, AUTHOR = {D. Einstein and D. Lichtblau and A. Strzebonski and S. Wagon}, TITLE = {Frobenius numbers by lattice point enumeration}, note = {Preprint}, year = {2005}, } @Misc{4ti2, author = {Raymond Hemmecke and Ralf Hemmecke}, title = {4ti2 Version 1.1---Computation of {H}ilbert bases, {G}raver bases, toric {G}r{\"o}bner bases, and more}, howpublished = {Available at {\tt www.4ti2.de}}, month = sep, year = 2003 } @Misc{cocoa, author = {{CoCoA}Team}, title = {{{\hbox{\rm C\kern-.13em o\kern-.07em C\kern-.13em o\kern-.15em A}}}: a system for doing {C}omputations in {C}ommutative {A}lgebra}, howpublished ={Available at \/ {\tt cocoa.dima.unige.it}}, } @Unpublished {vanherick, AUTHOR = {Andrew Van Herick}, TITLE = {Theoretical and computational methods for lattice point enumeration in inside-out polytopes}, note = {MA thesis, San Francisco State University}, year = {2007. Available at {\tt http://math.sfsu.edu/beck/teach/masters/andrewv.pdf}. \\ {\it Software package} {\tt IOP} available at {\tt http://iop.sourceforge.net/}} } @Unpublished {lisonekquasipol, AUTHOR = {Petr Lison$\check{\rm e}$k}, TITLE = {Combinatorial families enumerated by quasi-polynomials}, note = {Preprint (2006), to appear in \emph{J. Combin. Theory Ser. A}}, } @Unpublished {huthesis, AUTHOR = {Shubin Hu}, TITLE = {Shintain cocycles and generalized {D}edekind sums}, note = {Ph.D.\ thesis, University of Pennsylvania (1997)}, } @Unpublished {brownetalfrobenius, AUTHOR = {Alexander Brown and Eleandor Dannenberg and Jennifer Fox and Joshua Hanna and Katherine Keck and Alexander Moore and Zachary Robbins and Brandon Samples and James Stankewicz}, TITLE = {On a generalization of the {F}robenius number}, note = {Preprint ({\tt arXiv:1001.0207v2})}, year = 2010 } @article {stapledonadditive, AUTHOR = {Stapledon, Alan}, TITLE = {Additive number theory and inequalities in {E}hrhart theory}, JOURNAL = {Int. Math. Res. Not.}, FJOURNAL = {International Mathematics Research Notices. IMRN}, YEAR = {2016}, NUMBER = {5}, PAGES = {1497--1540}, ISSN = {1073-7928}, MRCLASS = {11H06 (11B30)}, MRNUMBER = {3509934}, DOI = {10.1093/imrn/rnv186}, URL = {http://dx.doi.org/10.1093/imrn/rnv186}, } @article {stapledonfreesums, AUTHOR = {Stapledon, Alan}, TITLE = {Counting lattice points in free sums of polytopes}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {151}, YEAR = {2017}, PAGES = {51--60}, ISSN = {0097-3165}, MRCLASS = {52B20}, MRNUMBER = {3663488}, MRREVIEWER = {Matthias Beck}, DOI = {10.1016/j.jcta.2017.04.004}, URL = {https://doi.org/10.1016/j.jcta.2017.04.004}, } @Unpublished {konvalinkapakcayleypolytopes, AUTHOR = {Matjaz Konvalinka and Igor Pak}, TITLE = {Triangulations of {C}ayley and {T}utte polytopes}, note = {Preprint ({\tt arXiv:1108.1905v1})}, year = 2011 } @Unpublished {braundavis, AUTHOR = {Benjamin Braun and Robert Davis}, TITLE = {Ehrhart series, unimodality, and integrally closed reflexive polytopes}, note = {Preprint ({\tt arXiv:math/1403.5378})}, } @Unpublished {davissymmbirkhoff, AUTHOR = {Robert Davis}, TITLE = {Ehrhart series of polytopes related to symmetric doubly-stochastic matrices}, note = {Preprint ({\tt arXiv:math/1409.2742})}, } @Unpublished {corteelsavagesillseulermahonian, AUTHOR = {Sylvie Corteel and Carla D. Savage and Andrew V. Sills}, TITLE = {Lecture hall sequences, q-series, and asymmetric partition identities}, note = {Preprint, to appear in Developments in Mathematics, Springer}, year = 2011 } @Unpublished {brightsavage, AUTHOR = {Katie Bright and Carla D. Savage}, TITLE = {The geometry of lecture hall partitions and quadratic permutation statistics }, note = {Preprint}, year = 2011 } @Unpublished {cranstonantimagic, AUTHOR = {Daniel W. Cranston}, TITLE = {Regular graphs of odd degree are antimagic}, note = {Preprint ({\tt arXiv:1303.4850})}, } @article {robbinstribonacci, AUTHOR = {Robbins, Neville}, TITLE = {On {T}ribonacci numbers and 3-regular compositions}, JOURNAL = {Fibonacci Quaterly}, VOLUME = {52}, YEAR = {2014}, PAGES = {16--19}, } @Unpublished{robbinstribonaccigeneralized, AUTHOR = {Robbins, Neville}, TITLE = {On $r$-regular compositions}, JOURNAL = {Journal for Combinatorial Mathematics and Combinatorial Computing}, YEAR = {Journal for Combinatorial Mathematics and Combinatorial Computing, to appear}, } @article {ardilacastillohenley, AUTHOR = {Ardila, Federico and Castillo, Federico and Henley, Michael}, TITLE = {The arithmetic {T}utte polynomials of the classical root systems}, JOURNAL = {Int. Math. Res. Not. IMRN}, FJOURNAL = {International Mathematics Research Notices. IMRN}, YEAR = {2015}, NUMBER = {12}, PAGES = {3830--3877}, ISSN = {1073-7928}, MRCLASS = {05C31 (17B22)}, MRNUMBER = {3356740}, MRREVIEWER = {Seyed Amin Seyed Fakhari}, DOI = {10.1093/imrn/rnu050}, URL = {https://doi.org/10.1093/imrn/rnu050}, note = {{\tt arXiv:1305.6621}}, } @article {radcarlitz, AUTHOR = {Matthias Beck and Florian Kohl}, TITLE = {Rademacher--{C}arlitz polynomials}, JOURNAL = {Acta Arith.}, FJOURNAL = {Acta Arithmetica}, VOLUME = {163}, YEAR = {2014}, PAGES = {379--393}, note = {{\tt arXiv:1310.0380}}, } @article {comparithm, AUTHOR = {Matthias Beck and Neville Robbins}, TITLE = {Variations on a generating-function theme: {E}numerating compositions with parts avoiding an arithmetic sequence}, JOURNAL = {American Mathematical Monthly (to appear)}, note = {{\tt arXiv:1403.0665}}, } @article {fixeddiffpartitions, AUTHOR = {George E. Andrews and Matthias Beck and Neville Robbins}, TITLE = {Partitions with fixed differences between largest and smallest parts}, JOURNAL = {Proceedings of the AMS (to appear)}, note = {{\tt arXiv:1406.3374}}, } @article {signedpetersen, AUTHOR = {Matthias Beck and Erika Meza and Bryan Nevarez and Alana Shine and Michael Young}, TITLE = {The chromatic polynomials of signed {P}etersen graphs}, JOURNAL = {Involve (to appear)}, note = {{\tt arXiv:1311.1760}}, } @article {stanleysurvey, AUTHOR = {Matthias Beck}, TITLE = {Stanley's major contributions to {E}hrhart theory}, JOURNAL = {Festschrift in honor of Richard Stanley's 70th birthday, AMS (to appear)}, note = {{\tt arXiv:1407.0255}}, } @article {beulerian, AUTHOR = {Matthias Beck and Katharina Jochemko and Emily McCullough}, TITLE = {$h^*$-polynomials of zonotopes}, JOURNAL = {Transactions of the American Mathematical Society (to appear)}, note = {{\tt arXiv:1609.08596}}, } @article {ionnisfisikopoulos, AUTHOR = {Ionnis Z. Emiris and Vissarion Fisikopoulos}, TITLE = {Efficient random-walk methods for approximating polytope volume}, note = {Preprint ({\tt arXiv:1312.2873})}, } @article {haaseetalunimtriangpos, AUTHOR = {Christian Haase and Andreas Paffenholz and Lindsay C. Piechnik and Francisco Santos}, TITLE = {Existence of unimodular triangulations---positive results}, note = {Preprint ({\tt arXiv:1405.1687})}, } @manual{sagemath, Key = {SageMath}, Author = {Sage Developers, The }, Title = {{S}ageMath, the {S}age {M}athematics {S}oftware {S}ystem ({V}ersion 7.3)}, note = {{\tt http://www.sagemath.org}}, Year = {2016}, } @misc{jochemkoveronesesymm, title={Symmetric decompositions and the {V}eronese construction}, author={Katharina Jochemko}, note = {Preprint ({\tt arXiv:2004.05423})}, year={2021}, } @misc{batyrevkasprzykschaller, title={On the {F}ine Interior of Three-dimensional Canonical {F}ano Polytopes}, author={Victor Batyrev and Alexander Kasprzyk and Karin Schaller}, note = {Preprint ({\tt arXiv:1911.12048})}, year={2019}, } @misc{rationalbetkemcmullen, title={Decompositions of {E}hrhart $h^*$-polynomials for rational polytopes}, author={Matthias Beck and Benjamin Braun and Andr\'es R. Vindas-Mel\'endez}, note = {Preprint ({\tt arXiv:2006.10076})}, year={2021}, } @misc{hstarboundary, title={Boundary $h^*$-polynomials of rational polytopes}, author={Esme Bajo and Matthias Beck}, eprint = {2204.02568}, year={2022}, } @misc{athanasiadisinterior, title={Triangulations of simplicial complexes and theta polynomials}, author={Christos A. Athanasiadis}, eprint = {2209.01674}, year={2022}, } @article {eckhoffdimension, AUTHOR = {Eckhoff, J\"{u}rgen}, TITLE = {Combinatorial properties of {\(f\)}-vectors of convex polytopes}, JOURNAL = {Normat}, FJOURNAL = {Normat. Nordisk Matematisk Tidskrift}, VOLUME = {54}, YEAR = {2006}, NUMBER = {4}, PAGES = {146--159}, ISSN = {0801-3500}, MRCLASS = {52B05 (05E25)}, MRNUMBER = {2288936}, MRREVIEWER = {Jakob Jonsson}, } @misc{fstarvectors, title={Inequalities for $f^*$-vectors of Lattice Polytopes}, author={Matthias Beck and Danai Deligeorgaki and Max Hlavacek and Jerónimo Valencia-Porras}, eprint = {2210.12271}, year={2022}, } @misc{fernandespinaalfonsinrobins, title={On the period collapse of a family of {E}hrhart quasi-polynomials}, author={Cristina G. Fernandes and José C. de Pina and Jorge L. Ram\'irez Alfons\'in and Sinai Robins}, eprint = {2104.11025}, year={2021}, } @misc{hinman, author = {Hinman, Joshua}, keywords = {Combinatorics (math.CO), FOS: Mathematics, FOS: Mathematics}, title = {A Positive Answer to {Bárány's} Question on Face Numbers of Polytopes}, publisher = {arXiv}, eprint = {2204.02568}, year = {2022}, copyright = {arXiv.org perpetual, non-exclusive license} }