Shellability of chessboard complexes (Q1335149)

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.