CFDP 1458
Neighborhood Complexes and Generating Functions
Author(s):Publication Date: April 2004
Pages: 24
Abstract:
Given a1, a2,…,an in Zd, we examine the set, G, of all nonnegative integer combinations of these ai. In particular, we examine the generating function f(z) = Sum{b in G}zb. 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 Zn. 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.
Keywords:
Integer programming, Complex of maximal lattice free bodies, Generating functions
JEL Classification Codes: C61
See CFP: 1169