Combinatorics Seminar: "Equivalent notions to CL-shellability and EL-shellability"

Abstract: Just as Björner and Wachs introduced recursive atom orders (RAOs) and proved that a finite, bounded poset admits an RAO if and only if it is CL-shellable, we likewise introduce generalized recursive atom orders (GRAOs) and prove the equivalence of CC-shellability to having a GRAO.  We then show how any GRAO may be transformed into an RAO, thereby deducing equivalence of CL-shellability to CC-shellability.  Turning to EL-shellability, we prove that a finite bounded poset is EL-shellable if and only if it admits an RAO which is independent of choice of root.  Likewise we prove that a finite bounded poset is EC-shellable if and only if it admits a GRAO which is independent of choice of root.  We will review all these different notions of shellability as well as the notion of recursive atom order and what it means to be independent of choice of root, so as to make the talk accessible to non-specialists.  This is joint work with Grace Stadnyk.

Host: Martha Precup