Abstract
In this paper, we investigate the Castelnuovo-Mumford regularity of ordinary powers, integral closure of powers and symbolic powers of squarefree monomial ideals for certain cases. We provide a lower bound for regularity of all the ordinary powers, symbolic powers and integral closure of powers of edge ideals of hypergraphs in terms of induced matching number. We also prove that for certain classes of graphs, the regularity of the second symbolic power of their edge ideals coincides with that of their the second ordinary power.
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