Shifting operations and completely t–spread lexsegment ideals

In this article we introduce the concepts of arbitrary t–spread lexsegments and of arbitrary t–spread lexsegment ideals with t a positive integer. These concepts are a natural generalization of arbitrary lexsegments and arbitrary lexsegment ideals. An ideal generated by an arbitrary t–spread lexsegment is called completely t–spread lexsegment if it is equal to the intersection of an initial t–spread lexsegment ideal and of a final t–spread lexsegment ideal. We study the class of arbitrary t–spread lexsegment ideals. In particular, we characterize all completely t–spread lexsegment ideals. Moreover, we classify all completely t–spread lexsegment ideals with a linear resolution.