Mathematics Colloquia and Seminars
Return to Colloquia & Seminar listing
A quasi-polynomial q-Queens result and related Kronecker products of matricesAlgebra & 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.