Partial transposes of permutation matrices.
Permanents – a concise survey. (Permanenten – Ein kurzer Überblick.)
Permanents of Hessenberg -matrices revisited.
Permanents of Hessenberg (0,1)-matrices.
Proof of the alternating sign matrix conjecture.
Rational realization of the minimum ranks of nonnegative sign pattern matrices
A sign pattern matrix (or nonnegative sign pattern matrix) is a matrix whose entries are from the set (, respectively). The minimum rank (or rational minimum rank) of a sign pattern matrix is the minimum of the ranks of the matrices (rational matrices, respectively) whose entries have signs equal to the corresponding entries of . Using a correspondence between sign patterns with minimum rank and point-hyperplane configurations in and Steinitz’s theorem on the rational realizability of...
Refined counting of fully packed loop configurations.
Relationship of certain rings of infinite matrices over integers
Sia l'insieme degli interi non negativi e l'anello degli interi. Sia l'anello delle matrici su che hanno solo un numero finito di cifre non nulle in ogni linea ed in ogni colonna. Sia il sottoanello generato da e , dove (rispettivamente ) è ottenuto dalla matrice identità muovendo gli 1 una posizione a destra (rispettivamente in giù). Sia pure il sottoanello di generato da e . Infine sia il sottoanello delle matrici di che hanno solo un numero finito di cifre non nulle....
Remark to a problem on 0-1 matrices
Riordan arrays, orthogonal polynomials as moments, and Hankel transforms.
Sign patterns that require a positive or nonnegative left inverse.
Singular differences of powers of -matrices
Solving a family of permutation problems on 0-1 matrices
Subdeterminants and subgraphs
Sylvesterovy–Hadamardovy, Kravčukovy a Sylvesterovy–Kacovy matice
Je zcela běžné, že speciální třídy matic jsou pojmenovány podle matematika, který je buď poprvé představil nebo podstatně přispěl k jejich studiu. Článek je věnován třem třídám matic nesoucích ve svých názvech jména čtyř matematiků: Sylvesterovým–Hadamardovým maticím, Kravčukovým maticím a Sylvesterovým–Kacovým maticím. Přestože na první pohled nemají uvedené třídy příliš společného, jsou v textu ukázány jejich vzájemné souvislosti.
The Bernoullian of a Matrix. (A Generalization of the Bernoulli Numbers)
Si associano ad una matrice infinita di un certo tipo altre due matrici dello stesso tipo, dette rispettivamente bernoulliana e antibernoulliana di A. Si studiano alcune proprietà di queste matrici. Si ottiene in tal via una generalizzazione dei classici numeri di Bernoulli.
The Bruhat rank of a binary symmetric staircase pattern
In this work we show that the Bruhat rank of a symmetric (0,1)-matrix of order n with a staircase pattern, total support, and containing In, is at most 2. Several other related questions are also discussed. Some illustrative examples are presented.
The factorization of an integral matrix into a product of two integral symmetric matrices I
The inverse of the Pascal lower triangular matrix modulo .
The k-Fibonacci matrix and the Pascal matrix
We define the k-Fibonacci matrix as an extension of the classical Fibonacci matrix and relationed with the k-Fibonacci numbers. Then we give two factorizations of the Pascal matrix involving the k-Fibonacci matrix and two new matrices, L and R. As a consequence we find some combinatorial formulas involving the k-Fibonacci numbers.