Counting Nonattacking Chess Piece Placements: Bishops and Anassas

E. G. Santos

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arXiv · 2411.16492

Counting Nonattacking Chess Piece Placements: Bishops and Anassas

E. G. Santos

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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.

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E. G. Santos. 2024-11-25. Counting Nonattacking Chess Piece Placements: Bishops and Anassas. https://arxiv.org/abs/2411.16492

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