Discrete Math Seminar: Bennet Goeckner

  • Date: 09/17/2019
  • Time: 16:00
Bennet Goeckner, University of Washington

University of British Columbia


Resolving Stanley’s conjecture on k-fold acyclic complexes


In 1993, Stanley showed that if a simplicial complex is acyclic over some field, then its face poset can be decomposed into disjoint rank 1 boolean intervals whose minimal faces together form a subcomplex. Stanley further conjectured that complexes with a higher notion of acyclicity could be decomposed in a similar way using boolean intervals of higher rank. We provide an explicit counterexample to this conjecture. We also prove a special case of the conjecture, and show that a weaker decomposition into boolean trees always exists. This is joint work with Joseph Doolittle.

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Location: ESB 4127