Jeudi 8 janvier 2015 à 14h30 en salle C48

Claudia Malvenuto (Università di Roma)

Titre : Quasi-symmetric functions, poset partitions and finite topologies

Résumé :

A combinatorial Hopf algebra based on double posets, endowed with a
bilinear form based on pictures between double posets (in analogy to
pictures of tableaux as defined by Zelevinski) was introduced in 2011
by Malvenuto and Reutenauer.
When the second order of a double poset is total, one obtains the
notion of special double poset; it is equivalent to that of labelled
poset of Stanley. Its generating function, with respect to Stanley's
classical definition of P-partitions associated to a special poset P
is quasi-symmetric, and, in fact, it is a homomorphism between
the Hopf algebra of double posets and that of quasi-symmetric functions.
Generalizing to preorders, we define the notion of T-partitions
associated to a finite topology T, and deduce a Hopf algebra morphism
from a new Hopf algebra on topologies to the Hopf algebra of packed
words.

Remarques : Travaux communs avec L. Foissy et F. Patras.