On $t$-core towers and $t$-defects of partitions

Larry Rolen

On $t$-core towers and $t$-defects of partitions

Number Theory 2015-09-23 v1 Combinatorics

Authors: Larry Rolen

Abstract

We study generating functions which count the sizes of $t$ -cores of partitions, and, more generally, the sizes of higher rows in $t$ -core towers. We then use these results to derive an asymptotic for the average size of the $t$ -defect of partitions, as well as some curious congruences.

Keywords

t-cores t-core towers t-defects partitions generating functions asymptotics congruences

Cite

@article{arxiv.1509.06620,
  title  = {On $t$-core towers and $t$-defects of partitions},
  author = {Larry Rolen},
  journal= {arXiv preprint arXiv:1509.06620},
  year   = {2015}
}

Comments

12 pages

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