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 study a connection between these matrices and non-attacking q-rook placements, which leads to a combinatorial formula for the number Fλ (q) of matrices of fixed Jordan type as a weighted sum over rook placements.
Original language | English |
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Pages (from-to) | 1017-1028 |
Number of pages | 12 |
Journal | Discrete Mathematics and Theoretical Computer Science |
State | Published - 2013 |
Event | 25th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2013 - Paris, France Duration: Jun 24 2013 → Jun 28 2013 |
Keywords
- Jordan canonical form
- Nilpotent matrices
- Q-rook placements
- Set partitions
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science (all)
- Discrete Mathematics and Combinatorics