Add to ORKGThe set of n by n upper-triangular nilpotent matrices with entries in a finite field q 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\u27s lattice and non-attacking rook placements, which leads to a refinement of the formula for Fλ(q)
AbstractFor B∈Mm and C∈Mn we continue work in the direction of explicit determination of the Jordan ...
AbstractThe usual Jordan canonical form for matrices is extended first to nilpotent elements of the ...
Abstract. A classical conjecture by Graham Higman states that the number of conjugacy classes of Un(...
The set of upper-triangular nilpotent matrices with entries in a finite field $\mathbb{F}_q$ has Jor...
AbstractConnections betweenq-rook polynomials and matrices over finite fields are exploited to deriv...
AbstractWe give a counterexample to a conjecture about the possible Jordan normal forms of nilpotent...
AbstractAn algorithm to obtain a completion of a partial upper triangular matrices with prescribed e...
summary:A rook placement is a subset of a root system consisting of positive roots with pairwise non...
We consider the problem of finding the number of matrices over a finite field with a certain rank an...
AbstractWe give three interpretations of the number b of orbits of the Borel subgroup of upper trian...
A classical conjecture of Graham Higman states that the number of conjugacy classes in U_n(q), the g...
AbstractLet A ϵ Mn, B ϵ Mm, and λ ϵ C be given. For X ϵ Mn,m we seek to determine the Jordan structu...
We define a subsemigroup $S_n$ of the rook monoid $R_n$ and investigate its properties. To do this, ...
The $q$-Whittaker function $W_\lambda(\mathbf{x};q)$ associated to a partition $\lambda$ is a $q$-an...
In this note we give a new proof of a closed formula for the multivariable generating series of diag...
AbstractFor B∈Mm and C∈Mn we continue work in the direction of explicit determination of the Jordan ...
AbstractThe usual Jordan canonical form for matrices is extended first to nilpotent elements of the ...
Abstract. A classical conjecture by Graham Higman states that the number of conjugacy classes of Un(...
The set of upper-triangular nilpotent matrices with entries in a finite field $\mathbb{F}_q$ has Jor...
AbstractConnections betweenq-rook polynomials and matrices over finite fields are exploited to deriv...
AbstractWe give a counterexample to a conjecture about the possible Jordan normal forms of nilpotent...
AbstractAn algorithm to obtain a completion of a partial upper triangular matrices with prescribed e...
summary:A rook placement is a subset of a root system consisting of positive roots with pairwise non...
We consider the problem of finding the number of matrices over a finite field with a certain rank an...
AbstractWe give three interpretations of the number b of orbits of the Borel subgroup of upper trian...
A classical conjecture of Graham Higman states that the number of conjugacy classes in U_n(q), the g...
AbstractLet A ϵ Mn, B ϵ Mm, and λ ϵ C be given. For X ϵ Mn,m we seek to determine the Jordan structu...
We define a subsemigroup $S_n$ of the rook monoid $R_n$ and investigate its properties. To do this, ...
The $q$-Whittaker function $W_\lambda(\mathbf{x};q)$ associated to a partition $\lambda$ is a $q$-an...
In this note we give a new proof of a closed formula for the multivariable generating series of diag...
AbstractFor B∈Mm and C∈Mn we continue work in the direction of explicit determination of the Jordan ...
AbstractThe usual Jordan canonical form for matrices is extended first to nilpotent elements of the ...
Abstract. A classical conjecture by Graham Higman states that the number of conjugacy classes of Un(...