Resolving Stanley's conjecture on k-fold acyclic complexes

Joseph Doolittle, Bennet Goeckner

Research output: Contribution to journalArticlepeer-review


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 version of the conjecture for boolean trees and show that the original conjecture holds when this notion of acyclicity is as high as possible.
Original languageEnglish
Number of pages13
JournalCombinatorial Theory
Publication statusPublished - 15 Dec 2021


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