• Journal of the Korean Mathematical Society
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• v.55 no.4
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• pp.763-783
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• 2018

In this paper, we study an Artinian point-configuration quotient having the SLP. We show that an Artinian quotient of points in $\mathbb{p}^n$ has the SLP when the union of two sets of points has a specific Hilbert function. As an application, we prove that an Artinian linear star configuration quotient $R/(I_{\mathbb{X}}+I_{\mathbb{Y}})$ has the SLP if $\mathbb{X}$ and $\mathbb{Y}$ are linear starconfigurations in $\mathbb{p}^2$ of type s and t for $s{\geq}(^t_2)-1$ and $t{\geq}3$. We also show that an Artinian $\mathbb{k}$-configuration quotient $R/(I_{\mathbb{X}}+I_{\mathbb{Y}})$ has the SLP if $\mathbb{X}$ is a $\mathbb{k}$-configuration of type (1, 2) or (1, 2, 3) in $\mathbb{p}^2$, and $\mathbb{X}{\cup}\mathbb{Y}$ is a basic configuration in $\mathbb{p}^2$.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.541-548
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• 2006

We find a graded Artinian level O-sequence of the form $H\;:\;h_0\;h_1\;\cdots\;h_{d-1}\;h_d\cdots$ $^{(d+1-1_)-st}h_d$ < $h_{d+s}$ not having the Weak-Lefschetz property. We also introduce several algorithms for construction of some examples of non-unimodal level O-sequences using a computer program called CoCoA.