On the Asymptotic Linearity of Castelnuovo-mumford Regularity
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Castelnuovo-Mumford regularity of products of monomial ideals
Let $R=k[x_1,x_2,cdots, x_N]$ be a polynomial ring over a field $k$. We prove that for any positive integers $m, n$, $text{reg}(I^mJ^nK)leq mtext{reg}(I)+ntext{reg}(J)+text{reg}(K)$ if $I, J, Ksubseteq R$ are three monomial complete intersections ($I$, $J$, $K$ are not necessarily proper ideals of the polynomial ring $R$), and $I, J$ are of the form $(x_{i_1}^{a_1}, x_{i_2}^{a_2}, cdots, x_{i_l...
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It is shown that when a special vertex stretching is applied to a graph, the cochordal cover number of the graph increases exactly by one, as it happens to its induced matching number and (Castelnuovo-Mumford) regularity. As a consequence, it is shown that the induced matching number and cochordal cover number of a special vertex stretching of a graph G are equal provided G is well-covered bipa...
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Article history: Received 7 October 2016 Received in revised form 16 January 2017 Available online xxxx Communicated by S. Iyengar To the memory of our friend Tony Geramita MSC: 13D02; 13D40 We give a simple proof for the fact that the Castelnuovo–Mumford regularity and related invariants of products of powers of ideals are asymptotically linear in the exponents, provided that each ideal is gen...
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تاریخ انتشار 2002