| Autor: |
Hao, Robert X. J., Shen, Erin Y. Y. |
| Předmět: |
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| Zdroj: |
International Journal of Number Theory; Oct2021, Vol. 17 Issue 9, p2153-2173, 21p |
| Abstrakt: |
An l -regular overpartition of n is an overpartition of n into parts not divisible by l. Let A ¯ l (n) be the number of l -regular overpartitions of n. Andrews defined singular overpartitions counted by the partition function C ¯ k , i (n). It denotes the number of overpartitions of n in which no part is divisible by k and only parts ≡ ± i (mod k) may be overlined. He proved that C ¯ 3 , 1 (9 n + 3) and C ¯ 3 , 1 (9 n + 6) are divisible by 3. In this paper, we aim to introduce a crank of l -regular overpartitions for l ≥ 3 to investigate the partition function A ¯ l (n). We give combinatorial interpretations for some congruences of A ¯ l (n) including infinite families of congruences for A ¯ l (n) modulo 3 and 6 as well as the congruences of Andrews for C ¯ 3 , 1 (9 n + 3) and C ¯ 3 , 1 (9 n + 6). [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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