若干加权定向无间隙二部图的不交并的边理想的幂的正则性和投射维数
Regularity and projective dimension of powers of edge ideal of the disjoint union of some weighted oriented gap-free bipartite graphs
摘要：
本文给出了一类加权定向无隙二部图的不交并的边理想的幂的正则性的精确公式。对于这类边理想的投射维数，我们给出了它的精确公式。同时，我们也给出了这类边理想的高次幂的投射维数的上下界。算例表明，这些公式与方向选择有关。
英文摘要：
In this paper we provide some precise formulas for regularity of powers of edge ideal of the disjoint union of some weighted oriented gap-free bipartite graphs. For the projective dimension of such an edge ideal, we give its exact formula. Meanwhile, we also give the upper and lower bounds of projective dimension of higher power of such edge ideals. Some examples show that these formulas are related to direction selection.
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