10.46298/dmtcs.595
Boussicault, Adrien
Adrien
Boussicault
Operations on partially ordered sets and rational identities of type A
episciences.org
2013
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
contact@episciences.org
episciences.org
2009-02-13T00:00:00+01:00
2021-08-23T23:09:21+02:00
2013-04-07
en
Journal article
https://dmtcs.episciences.org/595
https://hal.archives-ouvertes.fr/hal-00980747v1
1365-8050
PDF
1
Discrete Mathematics & Theoretical Computer Science ; Vol. 15 no. 2 ; Combinatorics ; 1365-8050
Combinatorics
International audience
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.