Geodesic
Application of graph combinatorics to rational identities of type \(A\)
The electronic journal of combinatorics, Tome 16 (2009) no. 1
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

To a word $w$, we associate the rational function $\Psi_w = \prod (x_{w_i} - x_{w_{i+1}})^{-1}$. The main object, introduced by C. Greene to generalize identities linked to the Murnaghan-Nakayama rule, is a sum of its images by certain permutations of the variables. The sets of permutations that we consider are the linear extensions of oriented graphs. We explain how to compute this rational function, using the combinatorics of the graph $G$. We also establish a link between an algebraic property of the rational function (the factorization of the numerator) and a combinatorial property of the graph (the existence of a disconnecting chain).
DOI : 10.37236/234
Classification : 05E99, 05C38 
@article{10_37236_234,
     author = {Adrien Boussicault and Valentin F\'eray},
     title = {Application of graph combinatorics to rational identities of type {\(A\)}},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/234},
     zbl = {1237.05220},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/234/}
}
TY  - JOUR
AU  - Adrien Boussicault
AU  - Valentin Féray
TI  - Application of graph combinatorics to rational identities of type \(A\)
JO  - The electronic journal of combinatorics
PY  - 2009
VL  - 16
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.37236/234/
DO  - 10.37236/234
ID  - 10_37236_234
ER  - 
%0 Journal Article
%A Adrien Boussicault
%A Valentin Féray
%T Application of graph combinatorics to rational identities of type \(A\)
%J The electronic journal of combinatorics
%D 2009
%V 16
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/234/
%R 10.37236/234
%F 10_37236_234
Adrien Boussicault; Valentin Féray. Application of graph combinatorics to rational identities of type \(A\). The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/234

Cité par Sources :