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- W2795161821 abstract "The set of $n$ by $n$ upper-triangular nilpotent matrices with entries in a finite field $mathbb{F}_q$ has Jordan canonical forms indexed by partitions $lambda vdash n$. We present a combinatorial formula for computing the number $F_lambda(q)$ of matrices of Jordan type $lambda$ as a weighted sum over standard Young tableaux. We construct a bijection between paths in a modified version of Young's lattice and non-attacking rook placements, which leads to a refinement of the formula for $F_lambda(q)$." @default.
- W2795161821 created "2018-04-06" @default.
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- W2795161821 date "2018-03-29" @default.
- W2795161821 modified "2023-09-28" @default.
- W2795161821 title "Rook Placements and Jordan Forms of Upper-Triangular Nilpotent Matrices" @default.
- W2795161821 doi "https://doi.org/10.37236/6888" @default.
- W2795161821 hasPublicationYear "2018" @default.
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