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arXiv · 1402.2469

The edge ideals of complete multipartite hypergraphs

Dariush Kiani·Sara Saeedi Madani
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Abstract

We classify all complete uniform multipartite hypergraphs with respect to some algebraic properties, such as being (almost) complete intersection, Gorenstein, level, $l$-Cohen-Macaulay, $l$-Buchsbaum, unmixed, and satisfying Serre's condition $S_r$, via some combinatorial terms. Also, we prove that for a complete $s$-uniform $t$-partite hypergraph $H$, vertex decomposability, shellability, sequentially $S_r$ and sequentially Cohen-Macaulay properties coincide with the condition that $H$ has $t-1$ sides consisting of a single vertex. Moreover, we show that the latter condition occurs if and only if it is a chordal hypergraph.

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Dariush Kiani, Sara Saeedi Madani. 2014-02-11. The edge ideals of complete multipartite hypergraphs. https://arxiv.org/abs/1402.2469

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