| 书目名称 | Eulerian Numbers | | 编辑 | T. Kyle Petersen | | 视频video | | | 概述 | Offers a self-contained treatment of progress and problems related to the Eulerian numbers.Covers a topic that plays an important role in combinatorics, number theory, and topology.Provides previously | | 丛书名称 | Birkhäuser Advanced Texts‘ Basler Lehrbücher | | 图书封面 |  | | 描述 | .This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics include a thorough discussion of gamma-nonnegativity and real-rootedness for Eulerian polynomials, as well as the weak order and the shard intersection order of the symmetric group..The book also includes a parallel story of Catalan combinatorics, wherein the Eulerian numbers are replaced with Narayana numbers. Again there is a progression from combinatorics to geometry, including discussion of the associahedron and the lattice of noncrossing partitions..The final chapters discuss how both the Eulerian and Narayana numbers have analogues in any finite Coxeter group, with many of the same enumerative and geometric properties. Thereare four supplemental chapters throughout, which survey more advanced topics, including some open problems in combinatorial topology. .This textbook will serve a resource for experts in the field as well as for graduate | | 出版日期 | Textbook 2015 | | 关键词 | Catalan numbers; Coxeter groups; Eulerian numbers; Gal‘s conjecture; Gessel‘s conjecture; Narayana number | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4939-3091-3 | | isbn_softcover | 978-1-4939-4794-2 | | isbn_ebook | 978-1-4939-3091-3Series ISSN 1019-6242 Series E-ISSN 2296-4894 | | issn_series | 1019-6242 | | copyright | Springer Science+Business Media New York 2015 |
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发表于 2025-3-21 16:16:32
