Geodesic
Casting light on shadow Somos sequences
Glasgow mathematical journal, Tome 65 (2023), pp. S87-S101

Voir la notice de l'article provenant de la source Cambridge

DOI

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 $\mathbb{C}$-algebra of dual numbers from several different viewpoints: analytic formulae in terms of elliptic functions, linear difference equations, and Hankel determinants.
DOI : 10.1017/S0017089522000167
Mots-clés : Somos sequence, dual number, elliptic function, integrable map 
Hone, Andrew N. W. Casting light on shadow Somos sequences. Glasgow mathematical journal, Tome 65 (2023), pp. S87-S101. doi: 10.1017/S0017089522000167
@article{10_1017_S0017089522000167,
     author = {Hone, Andrew N. W.},
     title = {Casting light on shadow {Somos} sequences},
     journal = {Glasgow mathematical journal},
     pages = {S87--S101},
     year = {2023},
     volume = {65},
     number = {S1},
     doi = {10.1017/S0017089522000167},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089522000167/}
}
TY  - JOUR
AU  - Hone, Andrew N. W.
TI  - Casting light on shadow Somos sequences
JO  - Glasgow mathematical journal
PY  - 2023
SP  - S87
EP  - S101
VL  - 65
IS  - S1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089522000167/
DO  - 10.1017/S0017089522000167
ID  - 10_1017_S0017089522000167
ER  - 
%0 Journal Article
%A Hone, Andrew N. W.
%T Casting light on shadow Somos sequences
%J Glasgow mathematical journal
%D 2023
%P S87-S101
%V 65
%N S1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089522000167/
%R 10.1017/S0017089522000167
%F 10_1017_S0017089522000167

Cité par Sources :