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Abstract
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 present a combinatorial formula for computing the number Fλ(q) of matrices of Jordan type λ 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 Fλ(q).
Document Type
Article
Publication Date
3-29-2018
Funding Information
Simons Collaboration Grant 429920.
Repository Citation
Yip, Martha, "Rook Placements and Jordan Forms of Upper-Triangular Nilpotent Matrices" (2018). Mathematics Faculty Publications. 30.
https://uknowledge.uky.edu/math_facpub/30
Notes/Citation Information
Published in The Electronic Journal of Combinatorics, v. 25, issue 1, paper #P1.68, p. 1-25.
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