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

Larry Rolen

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arXiv · 1509.06620

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

Larry Rolen

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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.

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Larry Rolen. 2015-09-22. On $t$-core towers and $t$-defects of partitions. https://arxiv.org/abs/1509.06620

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