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 (...

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Prif Awdur:	Martha Yip
Fformat:	Artigo
Iaith:	Inglês
Cyhoeddwyd:	Discrete Mathematics & Theoretical Computer Science 2013-01-01
Cyfres:	Discrete Mathematics & Theoretical Computer Science
Pynciau:	q-rook placements jordan canonical form nilpotent matrices set partitions [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
Mynediad Ar-lein:	https://dmtcs.episciences.org/2362/pdf
Tagiau:	Ychwanegu Tag Dim Tagiau, Byddwch y cyntaf i dagio'r cofnod hwn!