Results 11 to 20 of about 205 (29)

Maximal Green Sequences of Exceptional Finite Mutation Type Quivers [PDF]

, 2014
Maximal green sequences are particular sequences of mutations of quivers which were introduced by Keller in the context of quantum dilogarithm identities and independently by Cecotti-C\'ordova-Vafa in the context of supersymmetric gauge theory.
Seven, Ahmet I.
core   +4 more sources

Natural Density of Rectangular Unimodular Integer Matrices [PDF]

, 2010
In this paper, we compute the natural density of the set of k x n integer matrices that can be extended to an invertible n x n matrix over the integers.
Maze, G., Rosenthal, J., Wagner, U.
core   +2 more sources

A generalization of Alternating Sign Matrices [PDF]

, 2013
In alternating sign matrices the first and last nonzero entry in each row and column is specified to be +1. Such matrices always exist. We investigate a generalization by specifying independently the sign of the first and last nonzero entry in each row
Brualdi, Richard A., Kim, Hwa Kyung
core   +1 more source

Natural Density Distribution of Hermite Normal Forms of Integer Matrices [PDF]

, 2011
The Hermite Normal Form (HNF) is a canonical representation of matrices over any principal ideal domain. Over the integers, the distribution of the HNFs of randomly looking matrices is far from uniform.
Maze, Gerard
core   +2 more sources

Inertia, positive definiteness and $\ell_p$ norm of GCD and LCM matrices and their unitary analogs [PDF]

, 2017
Let $S=\{x_1,x_2,\dots,x_n\}$ be a set of distinct positive integers, and let $f$ be an arithmetical function. The GCD matrix $(S)_f$ on $S$ associated with $f$ is defined as the $n\times n$ matrix having $f$ evaluated at the greatest common divisor of ...
Haukkanen, Pentti, Tóth, László
core   +2 more sources

On the connection between tridiagonal matrices, Chebyshev polynomials, and Fibonacci numbers

Acta Universitatis Sapientiae: Mathematica, 2020
In this note, we recall several connections between the determinant of some tridiagonal matrices and the orthogonal polynomials allowing the relation between Chebyshev polynomials of second kind and Fibonacci numbers.
da Fonseca Carlos M.
doaj   +1 more source

Jacobsons Lemma fails for nil-clean 2 × 2 integral matrices

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020
We show that for two 2 × 2 integral matrices A, B, if the product AB is nil-clean then BA may not be nil-clean. Despite the fact that for many special cases, BA is also nil-clean, we finally found three counterexamples.
Călugăreanu Grigore, Pop Horia F.
doaj   +1 more source

Rank relations between a {0, 1}-matrix and its complement

Open Mathematics, 2018
Let A be a {0, 1}-matrix and r(A) denotes its rank. The complement matrix of A is defined and denoted by Ac = J − A, where J is the matrix with each entry being 1.
Ma Chao, Zhong Jin
doaj   +1 more source

Generalized Pell Equations for 2 × 2 Matrices

Discussiones Mathematicae - General Algebra and Applications, 2017
In this paper we consider the solutions of the generalized matrix Pell equations X2 − dY2 = cI, where X and Y are 2 × 2 matrices over ℤ, d is a non-zero (positive or negative) square-free integer, c is an arbitrary integer and I is the 2 × 2 identity ...
Cohen Boaz
doaj   +1 more source

On Generalized Jacobsthal and Jacobsthal-Lucas polynomials

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016
In this paper we introduce a generalized Jacobsthal and Jacobsthal-Lucas polynomials, Jh,n and jh,n, respectively, that consist on an extension of Jacobsthal's polynomials Jn(𝑥) and Jacobsthal-Lucas polynomials jn(𝑥).
Catarino Paula, Morgado Maria Luisa
doaj   +1 more source