Geodesic
Ideals Generated by Reverse Lexicographic Segments
Matematičeskie zametki, Tome 89 (2011) no. 1, pp. 53-69

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Let $k$ be a field, and let $S=k[x_1,\dots,x_n]$ be the polynomial ring in $x_1,\dots,x_n$ with coefficients in the field $k$. We study ideals of $S$ which are generated by reverse lexicographic segments of monomials of $S$. An ideal generated by a reverse lexicographic segment is called a completely reverse lexicographic segment ideal if all iterated shadows of the set of generators are reverse lexicographic segments. We characterize all completely reverse lexicographic segment ideals of $S$ and determine conditions under which they have a linear resolution.
Keywords: polynomial ring, ideal, reverse lexicographic segment, iterated shadow, linear resolution. 
@article{MZM_2011_89_1_a5,
     author = {M. Crupi and M. La Barbiera},
     title = {Ideals {Generated} by {Reverse} {Lexicographic} {Segments}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {53--69},
     publisher = {mathdoc},
     volume = {89},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_89_1_a5/}
}
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M. Crupi; M. La Barbiera. Ideals Generated by Reverse Lexicographic Segments. Matematičeskie zametki, Tome 89 (2011) no. 1, pp. 53-69. http://geodesic.mathdoc.fr/item/MZM_2011_89_1_a5/