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

P. Hersh; J. Shareshian; D. Stanton

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

P. Hersh, J. Shareshian, D. Stanton

School of Mathematics

Research output: Contribution to conference › Paper › peer-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 language	English (US)
Pages	465-478
Number of pages	14
State	Published - Dec 1 2009
Event	21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09 - Linz, Austria Duration: Jul 20 2009 → Jul 24 2009

Other

Other	21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09
Country/Territory	Austria
City	Linz
Period	7/20/09 → 7/24/09

Keywords

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

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N2 - 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.

AB - 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.

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KW - Homology basis

KW - Plane partitions

KW - Q = -1 phenomenon

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ER -

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

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