English

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.

Keywords

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}
}
R2 v1 2026-07-22T17:36:02.717Z