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arXiv · 2606.24925

Invariants for a family of discrete equations with the Laurent property

Andrei K Svinin
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Abstract

Recently, we have found an infinite family of homogeneous discrete equations of odd order possessing the Laurent property. The first representative of this family is the well-known Somos-5 equation, which under certain conditions generates the integer sequence A006721, which has numerous applications. In this work, we construct a finite set of independent invariants for our equations. We show, through examples, that the presence of these invariants allows us to find a more general criterion for the integrality of sequences compared to what the usual Laurent property provides.

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Andrei K Svinin. 2026-06-21. Invariants for a family of discrete equations with the Laurent property. https://arxiv.org/abs/2606.24925

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