Integrable and superintegrable systems associated with multi-sums of products

TL;DR

This paper constructs and analyzes integrable and superintegrable systems linked to multi-sums of products, expanding the understanding of such systems in mathematical physics.

Contribution

It introduces new classes of integrable systems associated with multi-sums of products, highlighting their properties and integrability features.

Findings

Identification of Liouville integrable systems

Development of superintegrable systems related to multi-sums

Analysis of non-commutative integrability

Abstract

We construct and study certain Liouville integrable, superintegrable, and non-commutative integrable systems, which are associated with multi-sums of products.