New Ramanujan-type congruences for 4-core partitions
Colloquium Mathematicum, Tome 148 (2017) no. 1, pp. 157-164
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
A partition is called a $t$-core if none of its hook lengths is
divisible by $t$. Let $a_t(n)$ denote the number of $t$-cores of
$n$. We obtain two infinite families of congruences
modulo $5$ for $a_4(n)$. For example, we prove that for $\ell\geq 1$
and $n\geq 0$,
$$
a_4\biggl(5^{2\ell+1}n+\frac{21\cdot5^{2\ell}-5}{8}\biggr)\equiv 0\ ({\rm mod} 5).
$$
We also establish three infinite families of congruences modulo $4$.
Keywords:
partition called t core none its hook lengths divisible denote number t cores obtain infinite families congruences modulo example prove ell geq geq biggl ell frac cdot ell biggr equiv mod establish three infinite families congruences modulo
Affiliations des auteurs :
Ying-Ying Gao 1 ; Su-Ping Cui 2 ; Litao Guo 3 ; Bernard Lishuang Lin 4
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author = {Ying-Ying Gao and Su-Ping Cui and Litao Guo and Bernard Lishuang Lin},
title = {New {Ramanujan-type} congruences for 4-core partitions},
journal = {Colloquium Mathematicum},
pages = {157--164},
publisher = {mathdoc},
volume = {148},
number = {1},
year = {2017},
doi = {10.4064/cm6944-5-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm6944-5-2016/}
}
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Ying-Ying Gao; Su-Ping Cui; Litao Guo; Bernard Lishuang Lin. New Ramanujan-type congruences for 4-core partitions. Colloquium Mathematicum, Tome 148 (2017) no. 1, pp. 157-164. doi: 10.4064/cm6944-5-2016
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