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.
2010
01 Pubblicazione su rivista::01a Articolo in rivista
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/9466
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