A quasi-additive property of homological shift ideals
Abstract
In this paper, we investigate which classes of monomial ideals have a quasi-additive property of homological shift ideals. More precisely, for a monomial ideal I we are interested to find out whether HSi+j(I)⊂eq HSi(HSj(I)). It turns out that c-bounded principal Borel ideals as well as polymatroidal ideals satisfying strong exchange property, and polymatroidal ideals generated in degree two have this quasi-additive property. For squarefree Borel ideals, we even have equality. Besides, the inclusion holds for every equigenerated Borel ideal and polymatroidal ideal when j=1.
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