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

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 $λ \vdash n$. 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.
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Conference papers

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### Citation

Martha Yip. q-Rook placements and Jordan forms of upper-triangular nilpotent matrices. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.1017-1028, ⟨10.46298/dmtcs.2362⟩. ⟨hal-01229691⟩

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