38 research outputs found

    Cohen-Macaulay binomial edge ideals

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    We study the depth of classes of binomial edge ideals and classify all closed graphs whose binomial edge ideal is Cohen--Macaulay.Comment: 9 page

    Binomial edge ideals and rational normal scrolls

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    Let XX be the Hankel matrix of size 2×n2\times n and let GG be a closed graph on the vertex set [n].[n]. We study the binomial ideal IGK[x1,,xn+1]I_G\subset K[x_1,\ldots,x_{n+1}] which is generated by all the 22-minors of XX which correspond to the edges of G.G. We show that IGI_G is Cohen-Macaulay. We find the minimal primes of IGI_G and show that IGI_G is a set theoretical complete intersection. Moreover, a sharp upper bound for the regularity of IGI_G is given

    A note on the regularity of Hibi rings

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    We compute the regularity of the Hibi ring of any finite distributive lattice in terms of its poset of join irreducible elements.Comment: 5 pages, 2 figure