Gin and Lex of certain monomial ideals
Satoshi Murai, Takayuki Hibi
Abstract
Let A = K[x1, ..., xn] denote the polynomial ring in n variables over a field K of characteristic 0 with each °xi = 1. Given arbitrary integers i and j with 2 ≤ i ≤ n and 3 ≤ j ≤ n, we will construct a monomial ideal I ⊂ A such that (i) βk(I) < βk((I)) for all k < i, (ii) βi(I) = βi((I)), (iii) β((I)) < β((I)) for all < j and (iv) βj((I)) = βj((I)), where (I) is the generic initial ideal of I with respect to the reverse lexicographic order induced by x1 > >... > xn and where (I) is the lexsegment ideal with the same Hilbert function as I.
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