q-Rook placements and Jordan forms of upper-triangular nilpotent matrices
نویسنده
چکیده
The set of n by n upper-triangular nilpotent matrices with entries in a finite field Fq has Jordan canonical forms indexed by partitions λ ` n. We study a connection between these matrices and non-attacking q-rook placements, which leads to a combinatorial formula for the number Fλ(q) of matrices of fixed Jordan type as a weighted sum over rook placements. Résumé. L’ensemble des matrices triangulaires supérieures nilpotentes d’ordre n sur un corps fini Fq a des formes canoniques de Jordan indexées par les partitions λ ` n. Nous étudions une connexion entre ces matrices et les placements de tours, et nous présentons une formule combinatoire pour le nombre Fλ(q) des matrices comme une somme sur les placements de tours.
منابع مشابه
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