Martha Yip - q-Rook placements and Jordan forms of upper-triangular nilpotent matrices

dmtcs:2362 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.2362
q-Rook placements and Jordan forms of upper-triangular nilpotent matrices

Authors: Martha Yip 1

  • 1 University of Pennsylvania

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 $λ \vdash n$. We study a connection between these matrices and non-attacking q-rook placements, which leads to a combinatorial formula for the number$ F_λ (q)$ of matrices of fixed Jordan type as a weighted sum over rook placements.

https://doi.org/10.46298/dmtcs.2362
Source: HAL:hal-01229691v1
Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: q-rook placements,Jordan canonical form,nilpotent matrices,set partitions,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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