In this article, we introduce a new sequence (Formula presented.) to find a new estimation of the cardinality Nm of the minimal involutive square-free solution of level m. As an application, using the first values of (Formula presented.) we improve the estimations of Nm 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.

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

Castelli M.;Catino F.;Pinto G.
2020-01-01

Abstract

In this article, we introduce a new sequence (Formula presented.) to find a new estimation of the cardinality Nm of the minimal involutive square-free solution of level m. As an application, using the first values of (Formula presented.) we improve the estimations of Nm 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11587/446898
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