Return to Colloquia & Seminar listing

### 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.