Geodesic
Minimal Graded Resolutions of Reverse Lexsegment Ideals
Matematičeskie zametki, Tome 91 (2012) no. 3, pp. 383-399

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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 the minimal graded free $S$-resolutions of reverse lexsegment ideals of $S$. We discuss the extremal Betti numbers of initial reverse lexsegment ideals of $S$. Moreover, we analyze all reverse lexsegment ideals with linear resolution.
Keywords: polynomial ring, reverse lexsegment ideal, Betti number, monomial ideals, minimal graded free resolutions. 
@article{MZM_2012_91_3_a5,
     author = {M. Crupi and M. La Barbiera},
     title = {Minimal {Graded} {Resolutions} of {Reverse} {Lexsegment} {Ideals}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {383--399},
     publisher = {mathdoc},
     volume = {91},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_3_a5/}
}
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M. Crupi; M. La Barbiera. Minimal Graded Resolutions of Reverse Lexsegment Ideals. Matematičeskie zametki, Tome 91 (2012) no. 3, pp. 383-399. http://geodesic.mathdoc.fr/item/MZM_2012_91_3_a5/