New infinite families of congruences for 5-core and 7-core partitions

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发表日期：

2024年4月10日

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Z. Meng,
O. X. M. Yao

摘要

Let $a_t(n)$ $a_{t} (n)$ denote the number of t-core partitions of n. In recent years, a number of congruences for $a_t(n)$ $a_{t} (n)$ have been discovered for some small t. Very recently, Fathima and Pore [4] established infinite families of congruences modulo 3 for $a_5(n)$ $a_{5} (n)$ and congruences modulo 2 for $a_7(n)$ $a_{7} (n)$ . Motivated by their work, we prove some new infinite families of congruences modulo 3 for $a_5(n)$ $a_{5} (n)$ and congruences modulo 2 for $a_7(n)$ $a_{7} (n)$ by utilizing Newman's identities.