DOAJ Open Access 2009

Application of graph combinatorics to rational identities of type $A^\ast$

Adrien Boussicault Valentin Féray

Lihat Sumber DOI

Abstrak

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-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).

Topik & Kata Kunci

Mathematics

Penulis (2)

Adrien Boussicault

Valentin Féray

Format Sitasi

APA MLA BibTeX

Boussicault, A., Féray, V. (2009). Application of graph combinatorics to rational identities of type $A^\ast$. https://doi.org/10.46298/dmtcs.2722

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.2722

Informasi Jurnal

Tahun Terbit: 2009
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.2722
Akses: Open Access ✓