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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 |
Description
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.