On the ranks of configurations on the complete graphReport as inadecuate




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1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

Abstract : We consider the parameter rank introduced for graph configurations by M. Baker and S. Norine. We focus on complete graphs and obtain an efficient algorithm to determine the rank for these graphs. The analysis of this algorithm leads to the definition of a parameter on Dyck words, which we call prerank. We prove that the distribution of area and prerank on Dyck words of given length $2n$ leads to a polynomial with variables $q,t$ which is symmetric in these variables. This polynomial is different from the $q,t-$Catalan polynomial studied by A. Garsia, J. Haglund and M. Haiman.

Keywords : Rank Riemann-Roch for graphs Complete graphs Dyck Words





Author: Robert Cori - Yvan Le Borgne -

Source: https://hal.archives-ouvertes.fr/



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