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King}, Number = {3}, Pages = {263--281}, Title = {Unimodality and {L}ie superalgebras}, Volume = {72}, Year = {1985}} @inproceedings{Stanley1983, Author = {Stanley, Richard P.}, Booktitle = {Proceedings of the {I}nternational {C}ongress of {M}athematicians, {V}ol.\ 1, 2 ({W}arsaw, 1983)}, Mrclass = {14F25 (32C40 52A25)}, Mrnumber = {804700}, Mrreviewer = {P. McMullen}, Pages = {447--453}, Publisher = {PWN, Warsaw}, Title = {Combinatorial applications of the hard {L}efschetz theorem}, Year = {1984}} @article{Fristedt, Author = {Fristedt, Bert}, Doi = {10.2307/2154239}, Fjournal = {Transactions of the American Mathematical Society}, Issn = {0002-9947}, Journal = {Trans. Amer. Math. Soc.}, Mrclass = {11K99 (05A17 11P82)}, Mrnumber = {1094553}, Mrreviewer = {Jean-Loup Mauclaire}, Number = {2}, Pages = {703--735}, Title = {The structure of random partitions of large integers}, Url = {https://doi.org/10.2307/2154239}, Volume = {337}, Year = {1993}, Bdsk-Url-1 = {https://doi.org/10.2307/2154239}} @misc{JiangWang, Author = {Jiang, Tiefeng and Wang, Ke}, Date-Modified = {2019-05-24 17:30:58 +1000}, Eprint = {1805.06108}, Eprinttype = {arxiv}, Title = {A generalized {H}ardy--{R}amanujan formula for the number of restricted integer partitions}, Year = {2018}} @article{Romik, Author = {Romik, Dan}, Fjournal = {European Journal of Combinatorics}, Issn = {0195-6698}, Journal = {European J. Combin.}, Mrclass = {11P82}, Mrnumber = {2101031}, Number = {1}, Pages = {1--17}, Title = {Partitions of {$n$} into {$t\sqrt n$} parts}, Volume = {26}, Year = {2005}} @article{OHara1990, Author = {O'Hara, Kathleen M.}, Fjournal = {Journal of Combinatorial Theory. Series A}, Issn = {0097-3165}, Journal = {J. Combin. Theory Ser. A}, Mrclass = {05A99 (05A30 06A10 11P57)}, Mrnumber = {1031611}, Mrreviewer = {Christian Krattenthaler}, Number = {1}, Pages = {29--52}, Title = {Unimodality of {G}aussian coefficients: a constructive proof}, Volume = {53}, Year = {1990}} @article{PouzetRosenberg, Author = {M. Pouzet and I.G. Rosenberg}, Issn = {0195-6698}, Journal = {European Journal of Combinatorics}, Number = {4}, Pages = {349 - 370}, Title = {Sperner Properties for Groups and Relations}, Volume = {7}, Year = {1986}} @article{Proctor1982, Author = {Proctor, Robert A.}, Doi = {10.1137/0603026}, Fjournal = {Society for Industrial and Applied Mathematics. Journal on Algebraic and Discrete Methods}, Issn = {0196-5212}, Journal = {SIAM J. Algebraic Discrete Methods}, Mrclass = {06A10 (05A17 17B10)}, Mrnumber = {655567}, Mrreviewer = {J. B. 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Series A}, Issn = {0097-3165}, Journal = {J. Combin. Theory Ser. A}, Mrclass = {20C30 (05E10)}, Mrnumber = {3589885}, Mrreviewer = {Himmet Can}, Pages = {1--17}, Title = {Bounds on certain classes of {K}ronecker and {$q$}-binomial coefficients}, Volume = {147}, Year = {2017}} @article{PakPanova2013, Author = {Pak, Igor and Panova, Greta}, Fjournal = {Comptes Rendus Math\'ematique. Acad\'emie des Sciences. Paris}, Issn = {1631-073X}, Journal = {C. R. Math. Acad. Sci. Paris}, Mrclass = {05E10 (05A19 05E15)}, Mrnumber = {3090120}, Mrreviewer = {Vincenzo Chilla}, Number = {11-12}, Pages = {415--418}, Title = {Strict unimodality of {$q$}-binomial coefficients}, Volume = {351}, Year = {2013}} @article{Sylvester1878, Author = {Sylvester, J. J.}, Date-Added = {2018-04-09 16:18:24 +0000}, Date-Modified = {2018-04-09 16:18:24 +0000}, Journal = {Philos. Mag.}, Pages = {178 - 188}, Title = {Proof of the hitherto undemonstrated Fundamental Theorem of Invariants}, Volume = {5}, Year = {1878}} @article{Fristedt1993, Author = {Fristedt, Bert}, Doi = {10.2307/2154239}, Fjournal = {Transactions of the American Mathematical Society}, Issn = {0002-9947}, Journal = {Trans. Amer. Math. Soc.}, Mrclass = {11K99 (05A17 11P82)}, Mrnumber = {1094553}, Mrreviewer = {Jean-Loup Mauclaire}, Number = {2}, Pages = {703--735}, Title = {The structure of random partitions of large integers}, Url = {https://doi.org/10.2307/2154239}, Volume = {337}, Year = {1993}, Bdsk-Url-1 = {https://doi.org/10.2307/2154239}} @article{Szekeres1987, Author = {Szekeres, G.}, Doi = {10.1017/S0004972700026320}, Fjournal = {Bulletin of the Australian Mathematical Society}, Issn = {0004-9727}, Journal = {Bull. Austral. Math. Soc.}, Mrclass = {11P57}, Mrnumber = {897424}, Mrreviewer = {David M. 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Inference}, Mrclass = {60F05 (05A15 60C05 60J15)}, Mrnumber = {845921}, Mrreviewer = {Ira Gessel}, Number = {1}, Pages = {123--142}, Title = {Some asymptotic formulas for lattice paths}, Volume = {14}, Year = {1986}} @article{AlmkvistAndrews1991, Author = {Almkvist, Gert and Andrews, George E.}, Doi = {10.1016/0022-314X(91)90079-Q}, Fjournal = {Journal of Number Theory}, Issn = {0022-314X}, Journal = {J. Number Theory}, Mrclass = {11P82}, Mrnumber = {1111367}, Mrreviewer = {Matti Jutila}, Number = {2}, Pages = {135--144}, Title = {A {H}ardy-{R}amanujan formula for restricted partitions}, Url = {https://doi.org/10.1016/0022-314X(91)90079-Q}, Volume = {38}, Year = {1991}, Bdsk-Url-1 = {https://doi.org/10.1016/0022-314X(91)90079-Q}} @article{Szekeres1953, Author = {Szekeres, G.}, Doi = {10.1093/qmath/4.1.96}, Fjournal = {The Quarterly Journal of Mathematics. Oxford. Second Series}, Issn = {0033-5606}, Journal = {Quart. J. Math., Oxford Ser. (2)}, Mrclass = {10.0X}, Mrnumber = {0057279}, Mrreviewer = {J. Lehner}, Pages = {96--111}, Title = {Some asymptotic formulae in the theory of partitions. {II}}, Volume = {4}, Year = {1953}, Bdsk-Url-1 = {https://doi.org/10.1093/qmath/4.1.96}} @article{Szekeres1951, Author = {Szekeres, G.}, Doi = {10.1093/qmath/2.1.85}, Fjournal = {The Quarterly Journal of Mathematics. Oxford. Second Series}, Issn = {0033-5606}, Journal = {Quart. J. Math., Oxford Ser. (2)}, Mrclass = {10.0X}, Mrnumber = {0043129}, Mrreviewer = {J. Lehner}, Pages = {85--108}, Title = {An asymptotic formula in the theory of partitions}, Volume = {2}, Year = {1951}, Bdsk-Url-1 = {https://doi.org/10.1093/qmath/2.1.85}} @article{ErdosLehner1941, Author = {Erd{\"o}s, Paul and Lehner, Joseph}, Fjournal = {Duke Mathematical Journal}, Issn = {0012-7094}, Journal = {Duke Math. J.}, Mrclass = {10.0X}, Mrnumber = {0004841}, Mrreviewer = {R. D. James}, Pages = {335--345}, Title = {The distribution of the number of summands in the partitions of a positive integer}, Url = {http://projecteuclid.org/euclid.dmj/1077492649}, Volume = {8}, Year = {1941}, Bdsk-Url-1 = {http://projecteuclid.org/euclid.dmj/1077492649}} @article{HardyRamanujan1918, Author = {Hardy, G. H. and Ramanujan, S.}, Date-Modified = {2019-05-24 17:30:31 +1000}, Doi = {10.1112/plms/s2-17.1.75}, Fjournal = {Proceedings of the London Mathematical Society. Second Series}, Issn = {0024-6115}, Journal = {Proc. London Math. Soc. (2)}, Mrclass = {DML}, Mrnumber = {1575586}, Pages = {75--115}, Title = {Asymptotic {F}ormulae in {C}ombinatory {A}nalysis}, Volume = {17}, Year = {1918}} @misc{MelczerPanovaPemantle2018, Author = {Melczer, S. and Panova, G. and Pemantle, R.}, Date-Modified = {2019-05-24 17:31:27 +1000}, Eprint = {1805.08375}, Eprinttype = {arxiv}, Title = {Counting partitions inside a rectangle}, Year = {2018}, Bdsk-Url-1 = {https://arxiv.org/abs/1805.08375}} @unpublished{Richmond2018, Author = {L. Bruce Richmond}, Eprint = {arXiv:1803.08548}, Title = {A {G}eorge {S}zekeres Formula for Restricted Partitions}, Url = {https://arxiv.org/abs/1803.08548}, Year = {2018}, Bdsk-Url-1 = {https://arxiv.org/abs/1803.08548}}