CU Algebraic Lie Theory Seminar

CU Algebraic Lie Theory Seminar
q-Rook placements and upper-triangular nilpotent matrices Martha Yip, University of Pennsylvania
April 30, 2013 Math 350 2-3pm	Abstract The set of n by n upper-triangular nilpotent matrices with entries in a finite field has Jordan canonical forms indexed by the partitions of n. We will look at a connection between these matrices and non-attacking rook placements, which leads to a combinatorial formula for the number of matrices of fixed Jordan type as a weighted sum over rook placements.

q-Rook placements and upper-triangular nilpotent matrices

Martha Yip, University of Pennsylvania

April 30, 2013

Math 350

2-3pm

Abstract

The set of n by n upper-triangular nilpotent matrices with entries in a finite field has Jordan canonical forms indexed by the partitions of n. We will look at a connection between these matrices and non-attacking rook placements, which leads to a combinatorial formula for the number of matrices of fixed Jordan type as a weighted sum over rook placements.