Dual Numbers, Weighted Quivers, and Extended Somos and Gale-Robinson Sequences

Valentin Ovsienko; Serge Tabachnikov

doi:10.1007/s10468-018-9779-3

Dual Numbers, Weighted Quivers, and Extended Somos and Gale-Robinson Sequences

Valentin Ovsienko
, Serge Tabachnikov

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We investigate a general method that allows one to construct new integer sequences extending existing ones. We apply this method to the classic Somos-4 and Somos-5, and the Gale-Robinson sequences, as well as to more general class of sequences introduced by Fordy and Marsh, and produce a great number of new sequences. The method is based on the notion of “weighted quiver”, a quiver with a ℤ-valued function on the set of vertices that obeys very special rules of mutation.

Original language	English (US)
Pages (from-to)	1119-1132
Number of pages	14
Journal	Algebras and Representation Theory
Volume	21
Issue number	5
DOIs	https://doi.org/10.1007/s10468-018-9779-3
State	Published - Oct 1 2018

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s10468-018-9779-3

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AU - Tabachnikov, Serge

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AB - We investigate a general method that allows one to construct new integer sequences extending existing ones. We apply this method to the classic Somos-4 and Somos-5, and the Gale-Robinson sequences, as well as to more general class of sequences introduced by Fordy and Marsh, and produce a great number of new sequences. The method is based on the notion of “weighted quiver”, a quiver with a ℤ-valued function on the set of vertices that obeys very special rules of mutation.

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Dual Numbers, Weighted Quivers, and Extended Somos and Gale-Robinson Sequences

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