Geodesic
Diagrammatic description of \(c\)-vectors and \(d\)-vectors of cluster algebras of finite type
Tomoki Nakanishi1 ; Salvatore Stella2
1Nagoya University
2North Carolina State University
The electronic journal of combinatorics, Tome 21 (2014) no. 1
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

We provide an explicit Dynkin diagrammatic description of the $c$-vectors and the $d$-vectors (the denominator vectors) of any cluster algebra of finite type with principal coefficients and any initial exchange matrix. We use the surface realization of cluster algebras for types $A_n$ and $D_n$, then we apply the folding method to $D_{n+1}$ and $A_{2n-1}$ to obtain types $B_n$ and $C_n$. Exceptional types are done by direct inspection with the help of a computer algebra software. We also propose a conjecture on the root property of $c$-vectors for a general cluster algebra.
DOI : 10.37236/3106
Classification : 13F60
Mots-clés : finite type cluster algebras, c-vectors, d-vectors

Tomoki Nakanishi  1   ; Salvatore Stella  2

1 Nagoya University
2 North Carolina State University 
@article{10_37236_3106,
     author = {Tomoki Nakanishi and Salvatore Stella},
     title = {Diagrammatic description of \(c\)-vectors and \(d\)-vectors of cluster algebras of finite type},
     journal = {The electronic journal of combinatorics},
     year = {2014},
     volume = {21},
     number = {1},
     doi = {10.37236/3106},
     zbl = {1327.13080},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/3106/}
}
TY  - JOUR
AU  - Tomoki Nakanishi
AU  - Salvatore Stella
TI  - Diagrammatic description of \(c\)-vectors and \(d\)-vectors of cluster algebras of finite type
JO  - The electronic journal of combinatorics
PY  - 2014
VL  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.37236/3106/
DO  - 10.37236/3106
ID  - 10_37236_3106
ER  - 
%0 Journal Article
%A Tomoki Nakanishi
%A Salvatore Stella
%T Diagrammatic description of \(c\)-vectors and \(d\)-vectors of cluster algebras of finite type
%J The electronic journal of combinatorics
%D 2014
%V 21
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/3106/
%R 10.37236/3106
%F 10_37236_3106
Tomoki Nakanishi; Salvatore Stella. Diagrammatic description of \(c\)-vectors and \(d\)-vectors of cluster algebras of finite type. The electronic journal of combinatorics, Tome 21 (2014) no. 1. doi: 10.37236/3106

Cité par Sources :