论文标题
超图的欧拉理想的程度和规律性
Degree and regularity of Eulerian ideals of hypergraphs
论文作者
论文摘要
我们定义了$ K $均匀的超图的Eulerian理想，并研究其学位和Castelnuovo- -Mumford的规律性。主要工具是从超图获得的理想基础的基础。我们在超图中定义了奇偶校验的概念，并表明欧拉理想的规律性等于此类边缘的最大基数。该学位的公式涉及一组$ t $ -join的顶点集合的基数。在完整的$ k $ - 明确超图和完整的等级$ 3 $的情况下，我们计算了学位和规律性的明确性。
We define the Eulerian ideal of a $k$-uniform hypergraph and study its degree and Castelnuovo--Mumford regularity. The main tool is a Gröbner basis of the ideal obtained combinatorially from the hypergraph. We define the notion of parity join in a hypergraph and show that the regularity of the Eulerian ideal is equal to the maximum cardinality of such a set of edges. The formula for the degree involves the cardinality of the set of sets of vertices, $T$, that admit a $T$-join. We compute the degree and regularity explicity in the cases of a complete $k$-partite hypergraph and a complete hypergraph of rank $3$.
