Problem of the Week
Hilton Memorial Lecture
Enumerative chess means counting arrangements of chess pieces, or chess-like pieces, under some rules. The archetype of such questions is the n-queens problem, where n queens are placed on an n×n board so no two attack each other; there is no known formula for the number of such arrangements as a function of n, and I doubt that anyone expects there can be one. Our problem is slightly different, and also more general. Our fundamental rule is that the pieces are identical and no piece attacks any other.
I will talk today about arranging pieces on an m×n board with one piece in each row, where m is fixed but n varies. Simple variations are to specify arbitrarily the number of pieces in each row.
This is part of a joint project with Seth Chaiken from Albany.