Vector Partition Functions and Generalized Dahmen-micchelli Spaces
نویسندگان
چکیده
This is the first of a series of papers on partition functions and the index theory of transversally elliptic operators. In this paper we only discuss algebraic and combinatorial issues related to partition functions. The applications to index theory will appear in [4]. Here we introduce a space of functions on a lattice which generalizes 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.
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