Counting Domineering Positions
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
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
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.
Full version: pdf,
(Concerned with sequences
Received March 11 2020; revised version received March 15 2020; March 22 2021.
Published in Journal of Integer Sequences,
April 18 2021.
Journal of Integer Sequences home page