P. Hersh ; J. Shareshian ; D. Stanton - The $q=-1$ phenomenon for bounded (plane) partitions via homology concentration

dmtcs:2716 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) - https://doi.org/10.46298/dmtcs.2716
The $q=-1$ phenomenon for bounded (plane) partitions via homology concentrationArticle

Authors: P. Hersh 1,2; J. Shareshian 3; D. Stanton 4

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.


Volume: DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
Section: Proceedings
Published on: January 1, 2009
Imported on: January 31, 2017
Keywords: plane partitions,discrete Morse theory,$q=-1$ phenomenon,homology basis,down operator,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Algebraic and topological combinatorics of posets; Funder: National Science Foundation; Code: 0500638
  • Enumerative, Algebraic and Topological Combinatorics; Funder: National Science Foundation; Code: 0604233
  • Combinatorics of Special Functions; Funder: National Science Foundation; Code: 0503660
  • Algebraic and topological combinatorics; Funder: National Science Foundation; Code: 0757935

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