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Saturation points on faces of a rational polyhedral cone

Akimichi Takemura·Ruriko Yoshida
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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.

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Akimichi Takemura, Ruriko Yoshida. 2007-04-11. Saturation points on faces of a rational polyhedral cone. https://arxiv.org/abs/math/0605479

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