Application of graph combinatorics to rational identities of type A

Adrien Boussicault, Valentin Féray

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 Murnaghan-…