Skip to Main content Skip to Navigation

# 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.
Keywords :
Document type :
Conference papers
Complete list of metadata

Cited literature [15 references]

https://hal.inria.fr/hal-01229672
Contributor : Alain Monteil Connect in order to contact the contributor
Submitted on : Tuesday, November 17, 2015 - 10:19:41 AM
Last modification on : Saturday, June 25, 2022 - 10:35:59 AM
Long-term archiving on: : Thursday, February 18, 2016 - 11:35:08 AM

### File

dmAS0156.pdf
Publisher files allowed on an open archive

### Citation

Robert Cori, yvan Le Borgne. On the ranks of configurations on the complete graph. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.659-670, ⟨10.46298/dmtcs.2332⟩. ⟨hal-01229672⟩

Record views

Files downloads