Year: 1994
Type: article
Abstract: On a $2m\times 2n$ chessboard, the maximum number of nonattacking kings that can be placed is $mn$, since each $2\times 2$ cell can have at most one king. Let $f_m(n)$ denote the number of ways that $mn$ nonattacking kings can be placed on a $2m\times 2n$ chessboard. The purpose of this paper is to prove the following result. Theorem. For each $m=1,2,3,\ldots $ there are constants $c_m>0$, $d_m$, and $0\le \theta_m < m+1$ such that $$f_m(n)= (c_mn+d_m)(m+1)^n+O(\theta_m^n)\qquad (n\to\infty).$$
DOI: 10.37236/1197
Author: Herbert S. Wilf
Institution: University of Pennsylvania
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: Office of Naval Research
OpenAlex ID: W1729440882