The ideal of maximal flags of a poset
Amin Nematbakhsh
TL;DR
This paper investigates the algebraic and homological properties of flag ideals derived from posets, providing characterizations of unmixed and Cohen-Macaulay cases, and analyzing their Betti numbers and resolutions.
Contribution
It introduces a comprehensive study of flag ideals of posets, including new characterizations and structural results on their Betti numbers and resolutions.
Findings
Characterization of unmixed and Cohen-Macaulay flag ideals
Structural results for multigraded Betti numbers
Criteria for flag ideals with linear resolutions
Abstract
We study algebraic and homological properties of facet ideals of order complexes of posets which we call ideals of maximal flags of posets or simply flag ideals. We characterize the unmixed and Cohen-Macaulay flag ideals of graded posets. We also give structural results for the multigraded Betti numbers of flag ideals of such posets. The structural results on multigraded Betti numbers of flag ideals are used to characterize the class of flag ideals with linear resolutions.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory