Authors: Jojić, Duško
Panina, Gaiane Yurevna
Vrećica, Siniša
Živaljević, Rade 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Generalized chessboard complexes and discrete Morse theory
Other Titles: Обобщённые шахматные комплексы и дискретная теория Морса
Journal: Chebyshevskii Sbornik
Volume: 21
Issue: 2
First page: 207
Last page: 227
Issue Date: 1-Jan-2020
Rank: M51
ISSN: 2226-8383
DOI: 10.22405/2226-8383-2020-21-2-207-227
Chessboard complexes and their generalizations, as objects, and Discrete Morse theory, as a tool, are presented as a unifying theme linking different areas of geometry, topology, algebra and combinatorics. Edmonds and Fulkerson bottleneck (minmax) theorem is proved and interpreted as a result about a critical point of a discrete Morse function on the Bier sphere Bier(K) of an associated simplicial complex K. We illustrate the use of “standard discrete Morse functions” on generalized chessboard complexes by proving a connectivity result for chessboard complexes with multiplicities. Applications include new Tverberg-Van Kampen-Flores type results for jwise disjoint partitions of a simplex.
Keywords: Bottleneck theorem | Chessboard complexes | Discrete Morse theorey | For citation | Tverberg-Van Kampen-Flores theorems
Publisher: State Lev Tolstoy Pedagogical University

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