Enumerating partitions arising in homotopy theory
Algebraic Topology
2022-05-11 v3 Combinatorics
Rings and Algebras
Abstract
We present an infinite family of recursive formulas that count binary integer partitions satisfying natural divisibility conditions and show that these counts are interrelated via partial sums. Moreover, we interpret the partitions we study in the language of graded polynomial rings and apply this to the mod Steenrod algebra to compute the free rank of certain homology modules in stable homotopy theory.
Cite
@article{arxiv.2107.01316,
title = {Enumerating partitions arising in homotopy theory},
author = {Scott M. Bailey and Donald M. Larson},
journal= {arXiv preprint arXiv:2107.01316},
year = {2022}
}
Comments
15 pages. Comments welcome!