Journal of Combinatorics
Volume 5 (2014)
The $q = -1$ phenomenon via homology concentration
Pages: 167 – 194
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.