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arXiv · 2201.04595

Shifting operations and completely $t$-spread lexsegment ideals

Antonino Ficarra·Marilena Crupi
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Abstract

In this paper 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.

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Antonino Ficarra, Marilena Crupi. 2022-01-12. Shifting operations and completely $t$-spread lexsegment ideals. https://arxiv.org/abs/2201.04595

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