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

被引：5

作者：

Castelli, Marco ^{[1
]}

Catino, Francesco ^{[1
]}

Pinto, Giuseppina ^{[1
]}

机构：

[1] Univ Salento, Dipartimento Matemat & Fis Ennio De Giorgi, Via Prov Lecce Arnesano, I-73100 Lecce, Italy

来源：

COMMUNICATIONS IN ALGEBRA | 2020年 / 48卷 / 06期

关键词：

Yang-Baxter equation; set-theoretic solution; cycle set; EXTENSIONS;

D O I：

10.1080/00927872.2020.1713328

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we introduce a new sequence 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 we improve the estimations of N-m obtained by Gateva-Ivanova and Cameron and 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.

引用

页码：2369 / 2381

页数：13

共 19 条

[11] Multipermutation Solutions of the Yang-Baxter Equation [J].