Casting light on shadow Somos sequences
Abstract
Recently Ovsienko and Tabachnikov considered extensions of Somos and Gale-Robinson sequences, defined over the algebra of dual numbers. Ovsienko used the same idea to construct so-called shadow sequences derived from other nonlinear recurrence relations exhibiting the Laurent phenomenon, with the original motivation being the hope that these examples should lead to an appropriate notion of a cluster superalgebra, incorporating Grassmann variables. Here we present various explicit expressions for the shadow of Somos-4 sequences, and describe the solution of a general Somos-4 recurrence defined over the -algebra of dual numbers from several different viewpoints: analytic formulae in terms of elliptic functions, linear difference equations, and Hankel determinants.
Cite
@article{arxiv.2111.10905,
title = {Casting light on shadow Somos sequences},
author = {Andrew N. W. Hone},
journal= {arXiv preprint arXiv:2111.10905},
year = {2021}
}