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

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.
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P. Hersh, J. Shareshian, D. Stanton. The $q=-1$ phenomenon for bounded (plane) partitions via homology concentration. 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. pp.465-478. ⟨hal-01185408⟩



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