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 results for the average size of the t-defect of partitions, as well as some curious congruences.
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Rolen, L. On t-Core Towers and t-Defects of Partitions. Ann. Comb. 21, 119–130 (2017). https://doi.org/10.1007/s00026-017-0343-3
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DOI: https://doi.org/10.1007/s00026-017-0343-3