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 Sponsored by the Meyer Fund
q-Rook placements and upper-triangular nilpotent matrices