The $q=-1$ phenomenon for bounded (plane) partitions via homology concentration
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 insta...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2009-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/2716/pdf |
| Summary: | 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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| ISSN: | 1365-8050 |