Title

Neighborhood Complexes and Generating Functions

Document Type

Discussion Paper

Publication Date

4-1-2004

CFDP Number

1458

CFDP Pages

24

Abstract

Given a 1 , a 2 ,…, a n in Z d , we examine the set, G , of all nonnegative integer combinations of these a i . In particular, we examine the generating function f ( z ) = Sum {b in G} z b . We prove that one can write this generating function as a rational function using the neighborhood complex (sometimes called the complex of maximal lattice-free bodies or the Scarf complex) on a particular lattice in Z n . In the generic case, this follows from algebraic results of D . Bayer and B. Sturmfels. Here we prove it geometrically in all cases, and we examine a generalization involving the neighborhood complex on an arbitrary lattice.

This document is currently not available here.

Share

COinS