The q = -1 phenomenon for bounded (plane) partitions via homology concentration

P. Hersh, J. Shareshian, D. Stanton

Research output: Contribution to conferencePaperpeer-review

Abstract

Algebraic complexes whose "faces" are indexed by partitions and plane partitions are introduced, and their homology is proven to be concentrated in even dimensions with homology basis indexed by fixed points of an involution, thereby explaining topologically two quite important instances of Stembridge's q = -1 phenomenon. A more general framework of invariant and coinvariant complexes with coefficients taken mod 2 is developed, and as a part of this story an analogous topological result for necklaces is conjectured.

Original languageEnglish (US)
Pages465-478
Number of pages14
StatePublished - Dec 1 2009
Event21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09 - Linz, Austria
Duration: Jul 20 2009Jul 24 2009

Other

Other21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09
CountryAustria
CityLinz
Period7/20/097/24/09

Keywords

  • Discrete Morse theory
  • Down operator
  • Homology basis
  • Plane partitions
  • Q = -1 phenomenon

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