Saturation points on faces of a rational polyhedral cone
Combinatorics
2008-06-02 v4 Statistics Theory
Statistics Theory
Abstract
Different commutative semigroups may have a common saturation. We consider distinguishing semigroups with a common saturation based on their ``sparsity''. We propose to qualitatively describe sparsity of a semigroup by considering which faces of the corresponding rational polyhedral cone have saturation points. For a commutative semigroup we give a necessary and sufficient condition for determining which faces have saturation points. We also show that we can construct a commutative semigroup with arbitrary consistent patterns of faces with saturation points.
Cite
@article{arxiv.math/0605479,
title = {Saturation points on faces of a rational polyhedral cone},
author = {Akimichi Takemura and Ruriko Yoshida},
journal= {arXiv preprint arXiv:math/0605479},
year = {2008}
}