Geodesic
Generalized chessboard complexes and discrete Morse theory
Čebyševskij sbornik, Tome 21 (2020) no. 2, pp. 207-227

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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 $j$-wise disjoint partitions of a simplex.
Keywords: chessboard complexes, discrete Morse theorey, bottleneck theorem, Tverberg-Van Kampen-Flores theorems. 
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     author = {D. Joji\'c and G. Panina and S. T. Vre\'cica and R. T. \v{Z}ivaljevi\'c},
     title = {Generalized chessboard complexes and discrete {Morse} theory},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {207--227},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a15/}
}
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D. Jojić; G. Panina; S. T. Vrećica; R. T. Živaljević. Generalized chessboard complexes and discrete Morse theory. Čebyševskij sbornik, Tome 21 (2020) no. 2, pp. 207-227. http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a15/