Abstract

We give a combinatorial condition that ensures a monomial ideal has a nonzero Betti number in a given multidegree. As a result, we combinatorially characterize all multigraded Betti numbers, projective dimension and regularity of facet ideals of simplicial forests. Our condition is expressed in terms of minimal facet covers of simplicial complexes.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.