Xavier Mart'inez-Rivera

activity

20162021

most citedClassification of families of pr- and epr-sequences

6 citations · 18 across the 5 of their papers we have counts for

collaborators

7 papers

math.CO2021

Combinatorial properties of the enhanced principal rank characteristic sequence over finite fields

Peter J. Dukes, Xavier Martínez-Rivera

The enhanced principal rank characteristic sequence (epr-sequence) of a symmetric matrix $B \in F^{n \times n}$ is defined as $ℓ_{1} ℓ_{2} \dots ℓ_{n}$ , where $\ell_j…

math.CO2020

On 0--1 matrices whose inverses have entries of the same modulus

Xavier Martínez-Rivera

A conjecture of Barrett, Butler and Hall may be stated as follows: If $n \geq 3$ and $A \in {0, 1}^{n \times n}$ (the family of $n \times n$ 0--1 matrices) is a nonsingular symmet…

math.CO2018

On the almost-principal minors of a symmetric matrix

Shaun M. Fallat, Xavier Martínez-Rivera

The almost-principal rank characteristic sequence (apr-sequence) of an $n \times n$ symmetric matrix is introduced, which is defined to be the string $a_{1} a_{2} \dots a_{n - 1}$ , where…

math.CO2017★ 2 cited

The quasi principal rank characteristic sequence

Shaun M. Fallat, Xavier Martínez-Rivera

A minor of a matrix is quasi-principal if it is a principal or an almost-principal minor. The quasi principal rank characteristic sequence (qpr-sequence) of an $n \times n$ symmetri…

math.CO2016★ 5 cited

The signed enhanced principal rank characteristic sequence

Xavier Martínez-Rivera

The signed enhanced principal rank characteristic sequence (sepr-sequence) of an $n \times n$ Hermitian matrix is the sequence $t_{1} t_{2} \dots t_{n}$ , where $t_{k}$ is either $A^{*}$ ,…

math.CO2016★ 5 cited

The enhanced principal rank characteristic sequence over a field of characteristic 2

Xavier Martínez-Rivera

The enhanced principal rank characteristic sequence (epr-sequence) of an $n \times n$ symmetric matrix over a field $F$ was recently defined as $\ell_1 \ell_2 \cdots \ell_…

math.CO2016★ 6 cited

Classification of families of pr- and epr-sequences

Xavier Martínez-Rivera

This paper establishes new restrictions for attainable enhanced principal rank characteristic sequences (epr-sequences). These results are then used to classify two related familie…