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Paper   IPM / M / 16397
School of Mathematics
  Title:   Multigraded minimal free resolutions of simplicial subclutters
  Author(s):  Mina Bigdeli (Joint with A. A. Yazdan Pour)
  Status:   Published
  Journal: J. Combin. Theory Ser. A
  Year:  2021
  Pages:   DOI: 10.1016/j.jcta.2020.105339
  Supported by:  IPM
This paper concerns the study of a class of clutters called simplicial subclutters. Given a clutter C and its simplicial subclutter D, we compare some algebraic properties and invariants of the ideals I, J associated to these two clutters, respectively. We give a formula for computing the (multi)graded Betti numbers of J in terms of those of I and some combinatorial data about D. As a result, we see that if C admits a simplicial subclutter, then there exists a monomial uI such that the (multi)graded Betti numbers of I+(u) can be computed through those of I. It is proved that the Betti sequence of any graded ideal with linear resolution is the Betti sequence of an ideal associated to a simplicial subclutter of the complete clutter. These ideals turn out to have linear quotients. However, they do not form all the equigenerated square-free monomial ideals with linear quotients. If C admits \varnothing as a simplicial subclutter, then I has linear resolution over all fields. Examples show that the converse is not true.

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