Zobrazeno 1 - 10
of 511
pro vyhledávání: '"Gallardo, Luis"'
We describe combinatorial properties of the defining row of a circulant Hadamard matrix by exploiting its orthogonality to subsequent rows, and show how to exclude several particular forms of these matrices.
Externí odkaz:
http://arxiv.org/abs/2406.10748
Autor:
Gallardo, Luis H.
Assume that $H$ is a circulant Hadamard matrix of order $n\geq 4$. We consider an appropriate stochastic matrix $S$ of order $n$ depending on $H$. This allows us to prove that $n = 4$. Thus, there are only $10$ circulant Hadamard matrices.
Externí odkaz:
http://arxiv.org/abs/2405.13033
Autor:
Gallardo, Luis H., Zelinsky, Joshua
In this note, we fix a gap in a proof of the first author that 28 is the only even perfect number which is the sum of two perfect cubes. We also discuss the situation for higher powers.
Externí odkaz:
http://arxiv.org/abs/2310.07077
We give all splitting bi-unitary perfect polynomials over the field $\mathbb{F}_4$ and some splitting ones over $\mathbb{F}_{p^2}$, if $p$ is an odd prime.
Comment: 10 pages
Comment: 10 pages
Externí odkaz:
http://arxiv.org/abs/2310.05540
We build a variant of Collatz Conjecture for polynomials over $\mathbb{F}_2$ and we prove that it is solved. By the way, we give several examples.
Comment: 16 pages
Comment: 16 pages
Externí odkaz:
http://arxiv.org/abs/2308.01181
Publikováno v:
Aportaciones Matematicas Investigacion 20 (2011) 109--115
We give necessary conditions for perfection of some families of odd numbers with special multiplicative forms. Extending earlier work of Steuerwald, Kanold, McDaniel et al.
Comment: Paper published in Aportaciones Matematicas Investigacion 20 (2
Comment: Paper published in Aportaciones Matematicas Investigacion 20 (2
Externí odkaz:
http://arxiv.org/abs/2304.04109
Autor:
Gallardo, Luis H.
We work an analogue of a classical arithmetic problem over polynomials. More precisely, we study the fixed points $F$ of the sum of divisors function $\sigma : F_2[x] \mapsto F_2[x]$ (defined \emph{mutatis mutandi} like the usual sum of divisors over
Externí odkaz:
http://arxiv.org/abs/2301.06218
We adapt (over $\mathbb{F}_2$) the general notions of multiplicative function, Dirichlet convolution and Inverse. We get some interesting results, namely necessary conditions for an odd binary polynomial to be perfect. Note that we are inspired by th
Externí odkaz:
http://arxiv.org/abs/2301.05248
We give all non splitting bi-unitary perfect polynomials over the prime field of two elements, which have only Mersenne polynomials as odd irreducible divisors.
Comment: 9 pages. arXiv admin note: text overlap with arXiv:1810.09697
Comment: 9 pages. arXiv admin note: text overlap with arXiv:1810.09697
Externí odkaz:
http://arxiv.org/abs/2204.13337
The paper is about an arithmetic problem in $\F_2[x]$. We give \emph{admissible} (necessary) conditions satisfied by a set of odd prime divisors of perfect polynomials over $\F_2$. This allows us to prove a new characterization of \emph{all} known pe
Externí odkaz:
http://arxiv.org/abs/2202.08126