Gin and Lex of certain monomial ideals
| dc.creator | Murai, Satoshi | |
| dc.creator | Hibi, Takayuki | |
| dc.date | 2005-09-18 | |
| dc.date | 2006-03-22 | |
| dc.date.accessioned | 2026-07-07T06:44:41Z | |
| dc.date.available | 2026-07-07T06:44:41Z | |
| dc.description | Let $A = K[x_1, ..., x_n]$ denote the polynomial ring in $n$ variables over a field $K$ of characteristic 0 with each $°x_i = 1$. Given arbitrary integers $i$ and $j$ with $2 \leq i \leq n$ and $3 \leq j \leq n$, we will construct a monomial ideal $I \subset A$ such that (i) $β_k(I) < β_k(\Gin(I))$ for all $k < i$, (ii) $β_i(I) = β_i(\Gin(I))$, (iii) $β_\ell(\Gin(I)) < β_\ell(\Lex(I))$ for all $\ell < j$ and (iv) $β_j(\Gin(I)) = β_j(\Lex(I))$, where $\Gin(I)$ is the generic initial ideal of $I$ with respect to the reverse lexicographic order induced by $x_1 > >... > x_n$ and where $\Lex(I)$ is the lexsegment ideal with the same Hilbert function as $I$. | |
| dc.description | 9 pages, minor grammatical changes | |
| dc.identifier | https://arxiv.org/abs/math/0509403 | |
| dc.identifier | http://arxiv.org/abs/math/0509403 | |
| dc.identifier | Math. Scand. 99 (2006), no. 1, 76--86 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102858 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13D02 | |
| dc.title | Gin and Lex of certain monomial ideals | |
| dc.type | text |