Rook placements and Jordan forms of upper-triangular nilpotent matrices
Combinatorics
2017-03-02 v1
Abstract
The set of n by n upper-triangular nilpotent matrices with entries in a finite field F_q has Jordan canonical forms indexed by partitions lambda of n. We present a combinatorial formula for computing the number F_\lambda(q) of matrices of Jordan type lambda as a weighted sum over standard Young tableaux. We also study a connection between these matrices and non-attacking rook placements, which leads to a refinement of the formula for F_\lambda(q).
Keywords
Cite
@article{arxiv.1703.00057,
title = {Rook placements and Jordan forms of upper-triangular nilpotent matrices},
author = {Martha Yip},
journal= {arXiv preprint arXiv:1703.00057},
year = {2017}
}
Comments
25 pages, 6 figures