COMPLETELY LEXSEGMENT IDEALS

In this paper we study ideals which are generated by lexsegments of mo nomials. In contrast to initial lexsegments, the shadow of an arbitrar y lexsegment is in general not again a lexsegment. An ideal generated by a lexsegment is called completely lexsegment, if all iterated shado ws of the set of generators are lexsegments. We characterize all compl etely lexsegment ideals and describe cases in which they have a linear resolution. We also prove a persistence theorem which states that all iterated shadows of a lexsegment are again lexsegments if the first s hadow has this property.