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Counting Domineering Positions

2019/09/26 by Svenja Huntemann, Huntemann, Svenja, Neil A. McKay +1
Computer Science · Economics, Econometrics and Finance · Psychology · #05C30 #05C57 (Secondary) #91A46 (Primary) #Artificial Intelligence in Games #Combinatorics (math.CO) #FOS: Mathematics #Gambling Behavior and Treatments #Sports Analytics and Performance

paper · pdf · doi:10.48550/arxiv.1909.12419

openalex publication_date 2019/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Domineering is a two player game played on a checkerboard in which one player places dominoes vertically and the other places them horizontally. We give bivariate generating polynomials enumerating Domineering positions by the number of each player's pieces. We enumerate all positions, maximal positions, and positions where one player has no move. Using these polynomials we count the number of positions that occur during alternating play. Our method extends to enumerating positions from mid-game positions and we include an analysis of a tournament game.

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