Dual numbers, weighted quivers, and extended Somos and Gale-Robinson sequences
Combinatorics
2017-05-05 v1
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 -valued function on the set of vertices that obeys very special rules of mutation.
Keywords
Cite
@article{arxiv.1705.01623,
title = {Dual numbers, weighted quivers, and extended Somos and Gale-Robinson sequences},
author = {Valentin Ovsienko and Serge Tabachnikov},
journal= {arXiv preprint arXiv:1705.01623},
year = {2017}
}