2017/05/03 by Ovsienko, Valentin, Tabachnikov, Serge
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1705.01623
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.