| Abstract: | In this paper we study the number M m;n of ways to place nonattacking pawns on an m x n chessboard. We find an upper bound for M m;n and consider a lower bound for M m;n by reducing this problem to that of tiling an (m+1)x(n+1) board with square tiles of size 1x1 and 2x2. Also, we use the transfer-matrix method to implement an algorithm that allows us to get an explicit formula for M m;n for given m. Moreover, we show that the double limit := lim m;n  (M m;n )1/mn exists and 2.25915263  n 2.26055675. Also, the true value of n isaround 2.2591535382327...AMS Subject Classification: 05A16, 05C50, 52C20, 82B20. |
