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A quasi-polynomial q-Queens result and related Kronecker products of matrices

Algebra & Discrete Mathematics

Speaker: Christopher Hanusa, Queens College
Location: 3240 MSB
Start time: Tue, May 12 2009, 2:10PM

For a fixed number of nonattacking queens placed on a square board of varying size, we show that the number of solutions is a quasipolynomial function of the size of the board using Ehrhart theory. This result generalizes to other real and fairy pieces on a polygonal board. Determining the period of each quasipolynomial function requires calculating the least common multiple of all subdeterminants of a matrix. This matrix has the form of a Kronecker product of a matrix involving the moves of the piece and the incidence matrix of a complete graph. Investigation of this quantity gives a new linear algebraic result proved using graph theory. No background knowledge is necessary to enjoy this talk.