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- W1636404150 abstract "It is unknown if an Artinian level O-sequence of codimension 3 and type $r (ge 2)$ is unimodal, while it is known that any Gorenstein O-sequence of codimension 3 is unimodal. We show that some Artinian non-unimodal O-sequence of codimension 3 cannot be level. We also find another non-level case: if some Artinian algebra $A$ of codimension 3 has the Hilbert function $$begin{matrix}H & : & h_0 & h_1 & ... & h_{d-1} & underbrace{h_d ... h_d}_{stext{-times}} & h_{d+s}, end{matrix} $$ such that $h_d<h_{d+s}$ and $sge 2$, then $A$ has a socle element in degree $d+s-2$, that is, $A$ is not level." @default.
- W1636404150 created "2016-06-24" @default.
- W1636404150 creator A5063259438 @default.
- W1636404150 date "2005-05-08" @default.
- W1636404150 modified "2023-09-27" @default.
- W1636404150 title "NON-LEVEL O-SEQUENCES OF CODIMENSION 3 AND DEGREE OF THE SOCLE ELEMENTS" @default.
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