Shellability of chessboard complexes
type: Item
instance of: scholarly article
title: Shellability of chessboard complexes
zbMATH Open document ID: 0828.57017
DOI: 10.1007/BF02772986
published in: Israel Journal of Mathematics
publication date: 1994-09-27T00:00:00Z
review text: The chessboard complex \(\Delta_{m,n}\) is the abstract simplicial complex consisting of the set of all non-taking rook configurations (that is, no two rooks on the same row or column) on a fixed chessboard of arbitrary size \(m \times n\). This complex appears in several interesting combinatorial situations as described in the introduction to the paper. In the paper, the author considers not only rectangular chessboards but also chessboards of various other shapes. He obtains new results on vertex decomposability of such combinatorially defined simplicial complexes. Vertex decomposability implies strong consequences for a simplicial complex like shellability, which again implies that it is homotopy Cohen-Macaulay and (at least in principle) that a distinguished homology basis can be constructed.
Mathematics Subject Classification ID: 57Q99
Mathematics Subject Classification ID: 52B99
Mathematics Subject Classification ID: 05B99
zbMATH DE Number: 645148
zbMATH Keywords: chessboard complex
zbMATH Keywords: abstract simplicial complex
zbMATH Keywords: vertex decomposability
zbMATH Keywords: shellability
zbMATH Keywords: homotopy Cohen-Macaulay
zbMATH Keywords: homology basis
author: Günter M. Ziegler
reviewed by: Vagn Lundsgaard Hansen
MaRDI profile type: Publication
cites work: Q3943579
cites work: Some combinatorial and algebraic properties of Coxeter complexes and Tits buildings
cites work: Q4012033
cites work: Chessboard Complexes and Matching Complexes
cites work: On Lexicographically Shellable Posets
cites work: The d-Step Conjecture and Its Relatives
cites work: Matching theory
cites work: Decompositions of Simplicial Complexes Related to Diameters of Convex Polyhedra
cites work: A Generalized van Kampen-Flores Theorem
cites work: The colored Tverberg's problem and complexes of injective functions
cites work: On geometric semilattices
full work available at URL: https://doi.org/10.1007/bf02772986
OpenAlex ID: W2147942906
description: scientific article; zbMATH DE number 645148