# Saturation points on faces of a rational polyhedral cone

@article{Takemura2006SaturationPO, title={Saturation points on faces of a rational polyhedral cone}, author={Akimichi Takemura and Ruriko Yoshida}, journal={arXiv: Combinatorics}, year={2006} }

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…

## 7 Citations

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This paper summarizes the results in [Takemura and Yoshida, 2007] and studies how the difference between the semigroup generated by columns of the design matrix for a common diagonal effect model and its saturation are distributed.

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