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- W2768002433 abstract "Let $S = K[x_1, ldots, x_n]$ denote the polynomial ring in $n$ variables over a field $K$ with each $deg x_i = 1$ and $I subset S$ a homogeneous ideal of $S$ with $dim S/I = d$. The Hilbert series of $S/I$ is of the form $h_{S/I}(lambda)/(1 - lambda)^d$, where $h_{S/I}(lambda) = h_0 + h_1lambda + h_2lambda^2 + cdots + h_slambda^s$ with $h_s neq 0$ is the $h$-polynomial of $S/I$. It is known that, when $S/I$ is Cohen--Macaulay, one has $reg(S/I) = deg h_{S/I}(lambda)$, where $reg(S/I)$ is the (Castelnuovo--Mumford) regularity of $S/I$. In the present paper, given arbitrary integers $r$ and $s$ with $r geq 1$ and $s geq 1$, a monomial ideal $I$ of $S = K[x_1, ldots, x_n]$ with $n gg 0$ for which $reg(S/I) = r$ and $deg h_{S/I}(lambda) = s$ will be constructed. Furthermore, we give a class of edge ideals $I subset S$ of Cameron--Walker graphs with $reg(S/I) = deg h_{S/I}(lambda)$ for which $S/I$ is not Cohen--Macaulay." @default.
- W2768002433 created "2017-11-17" @default.
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- W2768002433 creator A5091362971 @default.
- W2768002433 date "2017-11-06" @default.
- W2768002433 modified "2023-09-24" @default.
- W2768002433 title "Regularity and $h$-polynomials of monomial ideals" @default.
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- W2768002433 doi "https://doi.org/10.48550/arxiv.1711.02002" @default.
- W2768002433 hasPublicationYear "2017" @default.
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