Minimal Graded Resolutions of Reverse Lexsegment Ideals

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.