Summary: FINITENESS THEOREMS IN STOCHASTIC INTEGER
MATTHIAS ASCHENBRENNER AND RAYMOND HEMMECKE
Dedicated to the memory of C. St. J. A. Nash-Williams, 19322001.
Abstract. We study Graver test sets for families of linear multi-stage sto-
chastic integer programs with varying number of scenarios. We show that
these test sets can be decomposed into finitely many "building blocks", in-
dependent of the number of scenarios, and we give an effective procedure to
compute them. The paper includes an introduction to Nash-Williams' theory
of better-quasi-orderings, which is used to show termination of our algorithm.
We also apply this theory to finiteness results for Hilbert functions.
Part 1. Noetherian Orderings and Monomial Ideals 5
1. Preliminaries 5
2. Orderings 7
3. Noetherian Orderings 10
4. Strongly Noetherian Orderings 11
5. Nash-Williams Orderings 13
6. Applications to Hilbert Functions 16