16/09/2016, 09:30 — 10:20 — Room 6.2.38, Faculty of Sciences of the Universidade de Lisboa
Pasquale Petrullo, Università degli Studi della Basilicata
Kostka-Foulkes polynomials, raising operators and chip-firing game
By means of the chip-firing game, an analogue of the Young raising operators can be defined for any connected simple graph. This gives in turn an analogue of the Hall-Littlewood symmetric functions for each of such graphs, then an analogue of the Kostka-Foulkes polynomials for any connected simple graph. Starting form this combinatorial approach, a subset of Kostka-Foulkes polynomials is considered which is closed under mutiplication. The elements of this semigroup are indexed by vectors of nonnegative integers and satisfy an interesting recursive formula.
