Linear extension sums as valuations on cones

Adrien Boussicault (1, 2) , Valentin Féray (1) , Alain Lascoux (2) , Victor Reiner (3)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 LIGM - Laboratoire d'Informatique Gaspard-Monge
3 UMN-MATH - School of Mathematics

The geometric and algebraic theory of valuations on cones is applied to understand identities involving summing certain rational functions over the set of linear extensions of a poset.

Mots clés: posets; linear extensions; valuations of cones; semigroup rings

Domaines: Combinatoire [math.CO]

Adrien Boussicault, Valentin Féray, Alain Lascoux, Victor Reiner. Linear extension sums as valuations on cones. Journal of Algebraic Combinatorics, 2012, 35 (4), pp.573-610. ⟨10.1007/s10801-011-0316-2⟩. ⟨hal-00510517v2⟩