TY - JOUR
T1 - Dual Numbers, Weighted Quivers, and Extended Somos and Gale-Robinson Sequences
AU - Ovsienko, Valentin
AU - Tabachnikov, Serge
N1 - Publisher Copyright:
© 2018, Springer Science+Business Media B.V., part of Springer Nature.
PY - 2018/10/1
Y1 - 2018/10/1
N2 - 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-valued function on the set of vertices that obeys very special rules of mutation.
AB - 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-valued function on the set of vertices that obeys very special rules of mutation.
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U2 - 10.1007/s10468-018-9779-3
DO - 10.1007/s10468-018-9779-3
M3 - Article
AN - SCOPUS:85044201656
SN - 1386-923X
VL - 21
SP - 1119
EP - 1132
JO - Algebras and Representation Theory
JF - Algebras and Representation Theory
IS - 5
ER -