Title	Rook Placements and Jordan Forms
Creator	Yip, Martha
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2017-05-18T09:02
Description	The set of upper-triangular nilpotent matrices with entries in a finite field $\mathbb{F}_q$ has Jordan canonical forms indexed by the 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 then discuss connections between these matrices, non-attacking rook placements, and set partitions, which lead to a refinement of the formula for $F_\lambda(q)$.
Extent	18 minutes
Subject	Mathematics; Combinatorics; Group theory and generalizations
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: University of Kentucky
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2017-11-15
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0357941
URI	http://hdl.handle.net/2429/63595
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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