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

Valentin Ovsienko, Serge Tabachnikov

Research output: Contribution to journalArticle


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 languageEnglish (US)
Pages (from-to)1119-1132
Number of pages14
JournalAlgebras and Representation Theory
Issue number5
StatePublished - Oct 1 2018


All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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