q-Rook placements and Jordan forms of upper-triangular nilpotent matrices
Copyright policy )q-Rook placements and Jordan forms of upper-triangular nilpotent matrices
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.
- University of Pennsylvania United States
- University of Kentucky United States
nilpotent matrices, [info.info-dm] computer science [cs]/discrete mathematics [cs.dm], q-rook placements, Jordan form, Young tableaux, Combinatorial aspects of groups and algebras, jordan canonical form, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], set partitions, rook placements, QA1-939, Jordan canonical form, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), finite fields, Mathematics, Combinatorial identities, bijective combinatorics
nilpotent matrices, [info.info-dm] computer science [cs]/discrete mathematics [cs.dm], q-rook placements, Jordan form, Young tableaux, Combinatorial aspects of groups and algebras, jordan canonical form, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], set partitions, rook placements, QA1-939, Jordan canonical form, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), finite fields, Mathematics, Combinatorial identities, bijective combinatorics
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