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

Authors
• 1 CNRS, Laboratoire de Mathématiques U.F.R. Sciences Exactes et Naturelles Moulin de la Housse, BP 1039 51687, REIMS Cedex 2, France , REIMS Cedex 2 (France)
• 2 Pennsylvania State University, University Park, Department of Mathematics, State College, PA, 16802, USA , State College (United States)
Type
Published Article
Journal
Algebras and Representation Theory
Publisher
Springer Netherlands
Publication Date
Mar 19, 2018
Volume
21
Issue
5
Pages
1119–1132
Identifiers
DOI: 10.1007/s10468-018-9779-3
Source
Springer Nature
Keywords
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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {Z}$\end{document}-valued function on the set of vertices that obeys very special rules of mutation.