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Dual numbers, weighted quivers, and extended Somos and Gale-Robinson sequences by Ovsienko, Valentin; Tabachnikov, Serge is a scholarly article available to read on EtoBox.

What is Dual numbers, weighted quivers, and extended Somos and Gale-Robinson sequences about?

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 $\mathbb Z$-valued function on the set of vertices that obeys very special rules of mutation.

Author

Ovsienko, Valentin; Tabachnikov, Serge

Published

2017

Language

EN