In this paper we only discuss algebraic and combinatorial issues related to partition functions. We introduce a space of functions on a lattice which general- izes the space of quasi–polynomials satisfying the difference equations associated to cocircuits of a sequence of vectors X. This space F(X) contains the partition function PX. We prove a ”localization formula” for any f in F(X). In particular, this implies that the partition function PX is a quasi–polynomial on the sets c ? B(X) where c is a big cell and B(X) is the zonotope generated by the vectors in X.
Vector partition function and generalized Dahmen-Micchelli spaces / DE CONCINI, Corrado; Procesi, Claudio; Vergne, M.. - In: TRANSFORMATION GROUPS. - ISSN 1083-4362. - STAMPA. - 15:(2010), pp. 751-773. [10.1007/s00031-010-9102-9]
Vector partition function and generalized Dahmen-Micchelli spaces
DE CONCINI, Corrado;PROCESI, Claudio;
2010
Abstract
In this paper we only discuss algebraic and combinatorial issues related to partition functions. We introduce a space of functions on a lattice which general- izes the space of quasi–polynomials satisfying the difference equations associated to cocircuits of a sequence of vectors X. This space F(X) contains the partition function PX. We prove a ”localization formula” for any f in F(X). In particular, this implies that the partition function PX is a quasi–polynomial on the sets c ? B(X) where c is a big cell and B(X) is the zonotope generated by the vectors in X.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
