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arXiv · 1905.00003

How to Find New Characteristic-Dependent Linear Rank Inequalities using Binary Matrices as a Guide

Victor Peña·Humberto Sarria
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Abstract

In Linear Algebra over finite fields, a characteristic-dependent linear rank inequality is a linear inequality that holds by ranks of subspaces of a vector space over a finite field of determined characteristic, and does not in general hold over other characteristics. In this paper, we show a method to produce these inequalities using binary matrices with suitable ranks over different fields. In particular, for each $n\geq7$, we produce $2\left\lfloor \frac{n-1}{2}\right\rfloor -4$ characteristic-dependent linear rank inequalities over $n$ variables. Many of the inequalities obtained are new but some of them imply the inequalities presented in [1,9].

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Victor Peña, Humberto Sarria. 2019-04-29. How to Find New Characteristic-Dependent Linear Rank Inequalities using Binary Matrices as a Guide. https://arxiv.org/abs/1905.00003

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