Counting Nonattacking Chess Piece Placements: Bishops and Anassas
Combinatorics
2025-12-17 v2
Abstract
We derive recurrences and closed-form expressions for counting nonattacking placements of two types of chess pieces with unbounded straight-line moves, namely the bishop (two diagonal moves) and the anassa (one horizontal or vertical move and one diagonal move), placed on a standard square chessboard. Additionally, we obtain explicit expressions for the corresponding quasi-polynomial coefficients. The recurrences are derived by analyzing how nonattacking configurations attack a specific subset of board squares, employing a bijective argument to establish the relations. The main results are simplifications of known expressions for the bishop and a general counting formula for the anassa.
Cite
@article{arxiv.2411.16492,
title = {Counting Nonattacking Chess Piece Placements: Bishops and Anassas},
author = {E. G. Santos},
journal= {arXiv preprint arXiv:2411.16492},
year = {2025}
}