Adrien Boussicault ; Valentin Féray - Application of graph combinatorics to rational identities of type $A^\ast$

dmtcs:2722 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) - https://doi.org/10.46298/dmtcs.2722
Application of graph combinatorics to rational identities of type $A^\ast$Article

Authors: Adrien Boussicault 1; Valentin Féray 1

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).


Volume: DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
Section: Proceedings
Published on: January 1, 2009
Imported on: January 31, 2017
Keywords: posets,maps,Rational functions,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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