# On the ranks of configurations on the complete graph

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.
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Communication dans un congrès
Alain Goupil and Gilles Schaeffer. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), pp.659-670, 2013, DMTCS Proceedings

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https://hal.inria.fr/hal-01229672
Contributeur : Alain Monteil <>
Soumis le : mardi 17 novembre 2015 - 10:19:41
Dernière modification le : jeudi 11 janvier 2018 - 06:20:17
Document(s) archivé(s) le : jeudi 18 février 2016 - 11:35:08

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• HAL Id : hal-01229672, version 1

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Robert Cori, Yvan Le Borgne. On the ranks of configurations on the complete graph. Alain Goupil and Gilles Schaeffer. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), pp.659-670, 2013, DMTCS Proceedings. 〈hal-01229672〉

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