Abstract
In 2007, Vallette built a bridge across posets and operads by proving that an operad is Koszul if and only if the associated partition posets are Cohen-Macaulay. Both notions of being Koszul and being Cohen-Macaulay admit different refinements: our goal here is to link two of these refinements. We more precisely prove that any (basic-set) operad whose associated posets admit isomorphism-compatible CL-shellings admits a Poincare-Birkhoff-Witt basis. Furthermore, we give counterexamples to the converse.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have