Rook Placements and Jordan Forms of Upper-Triangular Nilpotent Matrices
نویسندگان
چکیده
منابع مشابه
q-Rook placements and Jordan forms of upper-triangular nilpotent matrices
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. Résumé. L’ensemble des matrices triang...
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Goldman, Joichi, and White proved a beautiful theorem showing that the falling factorial generating function for the rook numbers of a Ferrers board factors over the integers. Briggs and Remmel studied an analogue of rook placements where rows are replaced by sets of m rows called levels. They proved a version of the factorization theorem in that setting, but only for certain Ferrers boards. We...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2018
ISSN: 1077-8926
DOI: 10.37236/6888