Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The edge ideals of complete multipartite hypergraphs   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.

1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio