Q-Rook placements and Jordan forms of upper-triangular nilpotent matrices

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1 Scopus citations


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 languageEnglish
Pages (from-to)1017-1028
Number of pages12
JournalDiscrete Mathematics and Theoretical Computer Science
StatePublished - 2013
Event25th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2013 - Paris, France
Duration: Jun 24 2013Jun 28 2013


  • Jordan canonical form
  • Nilpotent matrices
  • Q-rook placements
  • Set partitions

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)
  • Discrete Mathematics and Combinatorics


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