Shellability of uncrossing posets and the CW poset property
Connections for Women Workshop: Geometric and Topological Combinatorics August 31, 2017 - September 01, 2017
Location: SLMath: Eisenbud Auditorium
Bruhat order
Electrical network
Shellability
poset topology
06D25 - Post algebras (lattice-theoretic aspects) [See also 03G20]
05C69 - Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
3-Hersh
Matthew Dyer’s proof that reflection orders give rise to EL-shellings for Bruhat order relied on the fact that the number of so-called ascending chains in a closed interval in Bruhat order is the leading coefficient in a polynomial closely related to the Kazhdan– Lusztig polynomial. We give a new, poset-theoretic proof that reflection orders yield EL-shellings for Bruhat order based on a characterization of cover relations in Bruhat order which may not be so well known. This perspective also enables us to prove a conjecture of Thomas Lam that face posets of stratified spaces of response matrices of electrical networks are dual EL-shellable and are CW posets.
3-Hersh
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