A $q$-Queens Problem. VI. The Bishops' Period
Combinatorics
2021-06-21 v4
Abstract
The number of ways to place nonattacking queens, bishops, or similar chess pieces on an square chessboard is essentially a quasipolynomial function of (by Part I of this series). The period of the quasipolynomial is difficult to settle. Here we prove that the empirically observed period 2 for three to ten bishops is the exact period for every number of bishops greater than 2. The proof depends on signed graphs and the Ehrhart theory of inside-out polytopes.
Cite
@article{arxiv.1405.3001,
title = {A $q$-Queens Problem. VI. The Bishops' Period},
author = {Thomas Zaslavsky and Seth Chaiken and Christopher R. H. Hanusa},
journal= {arXiv preprint arXiv:1405.3001},
year = {2021}
}
Comments
15 pp.; 12 pp. without white space. v2: Updated citations, rearranged authors. 12 pp. v3: Updated citations. Rm unnec special commands. v4: 13 pp. Rev title. Corrected error; rev abstract; minor rev