arXiv subjects

Indalecio Ruiz-Bolanos

Publications and source records attributed to Indalecio Ruiz-Bolanos.

3 recordsLinked to original sources

arXiv2026

Nonlinear Skew Quasi-Cyclic Codes

This article explores nonlinear analogues of skew quasi-cyclic codes of index~$\ell$, i.e., $\mathbb{F}_{q^m}[X;σ]$-submodules of $\left(\mathbb{F}_{q^m}[X;σ]/(X^n - 1)\right)^\ell$. After introducing nonlinear skew quasi-cyclic codes, we then determine the module structure of these codes by using a two-fold iteration of the Smith normal form of matrices over skew polynomial rings. We show that actually a single use of the Smith normal form will suffice to determine the elementary divisors of the code. Along the way, we also describe duals of our codes with respect to appropriately chosen inner products.

cs.IT↗

arXiv2023

Young tableau reconstruction via minors

The tableau reconstruction problem, posed by Monks (2009), asks the following. Starting with a standard Young tableau $T$, a 1-minor of $T$ is a tableau obtained by first deleting any cell of $T$, and then performing jeu de taquin slides to fill the resulting gap. This can be iterated to arrive at the set of $k$-minors of $T$. The problem is this: given $k$, what are the values of $n$ such that every tableau of size $n$ can be reconstructed from its set of $k$-minors? For $k=1$, the problem was recently solved by Cain and Lehtonen. In this paper, we solve the problem for $k=2$, proving the sharp lower bound $n \geq 8$. In the case of multisets of $k$-minors, we also give a lower bound for arbitrary $k$, as a first step toward a sharp bound in the general multiset case.

math.CO↗

arXiv2022

Klein cordial trees and odd cyclic cordial friendship graphs

For a graph $G$ and an abelian group $A$, a labeling of the vertices of $G$ induces a labeling of the edges via the sum of adjacent vertex labels. Hovey introduced the notion of an $A$-cordial vertex labeling when both the vertex and edge labels are as evenly distributed as possible. Much work has since been done with trees, hypertrees, paths, cycles, ladders, prisms, hypercubes, and bipartite graphs. In this paper we show that all trees are $\mathbb{Z}_2^2$-cordial except for $P_4$ and $P_5$. In addition, we give numerous results relating to $\mathbb{Z}_m$-cordiality of the friendship graph $F_n$. The most general result shows that when $m$ is an odd multiple of $3$, then $F_n$ is $\mathbb{Z}_m$-cordial for all $n$. We also give a general conjecture to determine when $F_n$ is $\mathbb{Z}_m$-cordial.

math.CO↗