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arXiv · 1512.01973

Isotonian Algebras

Mina Bigdeli·Jürgen Herzog·Takayuki Hibi·Ayesha Asloob Qureshi·Akihiro Shikama
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Abstract

To a pair $P$ and $Q$ of finite posets we attach the toric ring $K[P,Q]$ whose generators are in bijection to the isotone maps from $P$ to $Q$. This class of algebras, called isotonian, are natural generalizations of the so-called Hibi rings. We determine the Krull dimension of these algebras and for particular classes of posets $P$ and $Q$ we show that $K[P,Q]$ is normal and that their defining ideal admits a quadratic Gr\"obner basis.

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Mina Bigdeli, Jürgen Herzog, Takayuki Hibi, Ayesha Asloob Qureshi, Akihiro Shikama. 2015-12-07. Isotonian Algebras. https://arxiv.org/abs/1512.01973

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