# 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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Communication dans un congrès
Alain Goupil and Gilles Schaeffer. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), pp.1017-1028, 2013, DMTCS Proceedings

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Soumis le : mardi 17 novembre 2015 - 10:20:01
Dernière modification le : mardi 7 mars 2017 - 15:23:38
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• HAL Id : hal-01229691, version 1

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Martha Yip. q-Rook placements and Jordan forms of upper-triangular nilpotent matrices. Alain Goupil and Gilles Schaeffer. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), pp.1017-1028, 2013, DMTCS Proceedings. 〈hal-01229691〉

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