Results 1 to 10 of about 21 (20)

Generating functions for a lattice path model introduced by Deutsch

open access: yesSpecial Matrices, 2021
The lattice path model suggested by E. Deutsch is derived from ordinary Dyck paths, but with additional down-steps of size −3, −5, −7, . . . . For such paths, we find the generating functions of them, according to length, ending at level i, both, when ...
Prodinger Helmut
doaj   +1 more source

On Generalized Jacobsthal and Jacobsthal–Lucas Numbers

open access: yesAnnales Mathematicae Silesianae, 2022
Jacobsthal numbers and Jacobsthal–Lucas numbers are some of the most studied special integer sequences related to the Fibonacci numbers. In this study, we introduce one parameter generalizations of Jacobsthal numbers and Jacobsthal–Lucas numbers.
Bród Dorota, Michalski Adrian
doaj   +1 more source

On the smallest singular value in the class of unit lower triangular matrices with entries in [−a, a]

open access: yesSpecial Matrices, 2021
Given a real number a ≥ 1, let Kn(a) be the set of all n × n unit lower triangular matrices with each element in the interval [−a, a]. Denoting by λn(·) the smallest eigenvalue of a given matrix, let cn(a) = min {λ n(YYT) : Y ∈ Kn(a)}.
Altınışık Ercan
doaj   +1 more source

On idempotent stable range 1 matrices

open access: yesSpecial Matrices, 2022
We characterize the idempotent stable range 1, 2 × 2 matrices over commutative rings and in particular the integral matrices with this property. Several special cases and examples complete the subject.
Călugăreanu Grigore, Pop Horia F.
doaj   +1 more source

Some combinatorial matrices and their LU-decomposition

open access: yesSpecial Matrices, 2020
Three combinatorial matrices were considered and their LU-decompositions were found. This is typically done by (creative) guessing, and the proofs are more or less routine calculations.
Prodinger Helmut
doaj   +1 more source

Negative clean rings

open access: yesAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022
A ring is called negative clean if the negative (i.e., the additive inverse) of each clean element is also clean. Clean rings are negative clean.
Călugăreanu Grigore, Pop Horia F.
doaj   +1 more source

Multiple gcd-closed sets and determinants of matrices associated with arithmetic functions

open access: yesOpen Mathematics, 2016
Let f be an arithmetic function and S= {x1, …, xn} be a set of n distinct positive integers. By (f(xi, xj)) (resp. (f[xi, xj])) we denote the n × n matrix having f evaluated at the greatest common divisor (xi, xj) (resp. the least common multiple [xi, xj]
Hong Siao, Hu Shuangnian, Hong Shaofang
doaj   +1 more source

The integer cp-rank of 2 × 2 matrices

open access: yesSpecial Matrices, 2019
We show the cp-rank of an integer doubly nonnegative 2 × 2 matrix does not exceed 11.
Laffey Thomas, Šmigoc Helena
doaj   +1 more source

Inverses and eigenvalues of diamondalternating sign matrices

open access: yesSpecial Matrices, 2014
An n × n diamond alternating sign matrix (ASM) is a (0, +1, −1)-matrix with ±1 entries alternatingand arranged in a diamond-shaped pattern. The explicit inverse (for n even) or generalized inverse (for nodd) of a diamond ASM is derived.
Catral Minerva   +3 more
doaj   +1 more source

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