2013/10/26 by Hersh, Patricia, Shareshian, John, Stanton, Dennis
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1310.7066
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.