The q=-1 phenomenon via homology concentration
Combinatorics
2013-10-29 v1
Abstract
We introduce a homological approach to exhibiting instances of Stembridge's q=-1 phenomenon. This approach is shown to explain two important instances of the phenomenon, namely that of partitions whose Ferrers diagrams fit in a rectangle of fixed size and that of plane partitions fitting in a box of fixed size. 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 homological result for necklaces is conjectured.
Keywords
Cite
@article{arxiv.1310.7066,
title = {The q=-1 phenomenon via homology concentration},
author = {Patricia Hersh and John Shareshian and Dennis Stanton},
journal= {arXiv preprint arXiv:1310.7066},
year = {2013}
}