arXiv subjects

Giuseppina Pinto

Publications and source records attributed to Giuseppina Pinto.

2 recordsLinked to original sources

arXiv2019

On the indecomposable involutive set-theoretic solutions of the Yang-Baxter equation of prime-power size

We develop a method to construct all the indecomposable involutive set-theoretic solutions of the Yang-Baxter equation with a prime-power number of elements and cyclic permutation group. Moreover, we give a complete classification of the indecomposable ones having abelian permutation group and cardinality $pq$ (where $p$ and $q$ are prime numbers not necessarily distinct).

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arXiv2019

About a question of Gateva-Ivanova and Cameron on square-free set-theoretic solutions of the Yang-Baxter equation

In this paper, we introduce a new sequence $\bar{N}_m$ to find a new estimation of the cardinality $N_m$ of the minimal involutive square-free solution of level $m$. As an application, using the first values of $\bar{N}_m$, we improve the estimations of $N_m$ obtained by Gateva-Ivanova and Cameron and by Lebed and Vendramin. Following the approach of the first part, in the last section we construct several new counterexamples to the Gateva-Ivanova's Conjecture.

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