Squarefree Lexsegment Ideals with Linear Resolution
Vittoria Bonanzinga; Loredana Sorrenti
Bollettino dell'Unione Matematica Italiana (2008)
- Volume: 1, Issue: 1, page 275-291
- ISSN: 0392-4041
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topBonanzinga, Vittoria, and Sorrenti, Loredana. "Squarefree Lexsegment Ideals with Linear Resolution." Bollettino dell'Unione Matematica Italiana 1.1 (2008): 275-291. <http://eudml.org/doc/290493>.
@article{Bonanzinga2008,
abstract = {In this paper we determine all squarefree completely lexsegment ideals which have a linear resolution. Let $M_d$ denote the set of all squarefree monomials of degree $d$ in a polynomial ring $k[x_1, \ldots, x_n ]$ in $n$ variables over a field $k$. We order the monomials lexicographically such that $x_1 > x_2 > \ldots > x_n$, thus a lexsegment (of degree $d$) is a subset of $M_d$ of the form $L(u, v) = \\{w \in M_d: u \geq w \geq v\\}$ for some $u, v \in M_d$ con $u \geq v$. An ideal generated by a lexsegment is called a lexsegment ideal. We describe the procedure to determine when such an ideal has a linear resolution.},
author = {Bonanzinga, Vittoria, Sorrenti, Loredana},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {275-291},
publisher = {Unione Matematica Italiana},
title = {Squarefree Lexsegment Ideals with Linear Resolution},
url = {http://eudml.org/doc/290493},
volume = {1},
year = {2008},
}
TY - JOUR
AU - Bonanzinga, Vittoria
AU - Sorrenti, Loredana
TI - Squarefree Lexsegment Ideals with Linear Resolution
JO - Bollettino dell'Unione Matematica Italiana
DA - 2008/2//
PB - Unione Matematica Italiana
VL - 1
IS - 1
SP - 275
EP - 291
AB - In this paper we determine all squarefree completely lexsegment ideals which have a linear resolution. Let $M_d$ denote the set of all squarefree monomials of degree $d$ in a polynomial ring $k[x_1, \ldots, x_n ]$ in $n$ variables over a field $k$. We order the monomials lexicographically such that $x_1 > x_2 > \ldots > x_n$, thus a lexsegment (of degree $d$) is a subset of $M_d$ of the form $L(u, v) = \{w \in M_d: u \geq w \geq v\}$ for some $u, v \in M_d$ con $u \geq v$. An ideal generated by a lexsegment is called a lexsegment ideal. We describe the procedure to determine when such an ideal has a linear resolution.
LA - eng
UR - http://eudml.org/doc/290493
ER -
References
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