Martha Yip
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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)
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https://doi.org/10.46298/dmtcs.2362
q-Rook placements and Jordan forms of upper-triangular nilpotent matrices
Authors: Martha Yip 1
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Martha Yip
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.
Soffer, Andrew, 2016, Upper Bounds On The Number Of Conjugacy Classes In Unitriangular Groups, Journal Of Group Theory, 19, 6, pp. 1063-1095, 10.1515/jgth-2016-0016.