Vector partition function and generalized Dahmen-Micchelli spaces

TL;DR

This paper explores algebraic and combinatorial aspects of vector partition functions, laying the groundwork for future applications in index theory of transversally elliptic operators.

Contribution

It introduces new algebraic and combinatorial methods for analyzing vector partition functions, setting the stage for subsequent index theory applications.

Findings

Developed algebraic frameworks for partition functions

Analyzed combinatorial structures related to vector partitions

Established foundations for future index theory applications

Abstract

This is the first of two 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 a subsequent paper.