Rook placements and Jordan forms of upper-triangular nilpotent matrices
| Autor: | Martha Yip |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Applied Mathematics
Lattice (group) Triangular matrix Type (model theory) Nilpotent matrix Theoretical Computer Science Combinatorics Finite field Computational Theory and Mathematics Bijection FOS: Mathematics Discrete Mathematics and Combinatorics Young tableau Mathematics - Combinatorics Canonical form Geometry and Topology Combinatorics (math.CO) Mathematics::Representation Theory Mathematics |
| DOI: | 10.48550/arxiv.1703.00057 |
| Popis: | 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 lambda of 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 also study a connection between these matrices and non-attacking rook placements, which leads to a refinement of the formula for F_\lambda(q). Comment: 25 pages, 6 figures |
| Databáze: | OpenAIRE |
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