Journal of Integer Sequences, Vol. 24 (2021), Article 21.4.8

Counting Domineering Positions

Svenja Huntemann
Department of Mathematics and Physical Sciences
Concordia University of Edmonton
Edmonton, AB T5B 4E4

Neil Anderson McKay
Department of Mathematics and Statistics
University of New Brunswick
Saint John, NB E2L 4L5


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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(Concerned with sequences A000045 A000931 A007598 A028420 A030186 A033506 A054894 A286945 A287595 A288028 A332714 A332862 A332865.)

Received March 11 2020; revised version received March 15 2020; March 22 2021. Published in Journal of Integer Sequences, April 18 2021.

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