Adrien Boussicault - Operations on partially ordered sets and rational identities of type A

dmtcs:595 - Discrete Mathematics & Theoretical Computer Science, April 7, 2013, Vol. 15 no. 2 -
Operations on partially ordered sets and rational identities of type A

Authors: Adrien Boussicault 1

We consider the family of rational functions ψw= ∏( xwi - xwi+1 )-1 indexed by words with no repetition. We study the combinatorics of the sums ΨP of the functions ψw when w describes the linear extensions of a given poset P. In particular, we point out the connexions between some transformations on posets and elementary operations on the fraction ΨP. We prove that the denominator of ΨP has a closed expression in terms of the Hasse diagram of P, and we compute its numerator in some special cases. We show that the computation of ΨP can be reduced to the case of bipartite posets. Finally, we compute the numerators associated to some special bipartite graphs as Schubert polynomials.

Volume: Vol. 15 no. 2
Section: Combinatorics
Published on: April 7, 2013
Accepted on: June 9, 2015
Submitted on: February 13, 2009
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

Linked publications - datasets - softwares

Source : ScholeXplorer IsRelatedTo ARXIV 2005.06950
Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.2005.06950
  • 2005.06950
  • 10.48550/arxiv.2005.06950
(Co)homology theories for structured spaces arising from their corresponding poset

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