New congruences for $$\ell $$ -regular partitions for $$\ell \in \{5,6,7,49\}$$
Tóm tắt
We find several new congruences for
$$\ell $$
-regular partitions for
$$\ell \in \{5,6,7,49\}$$
and also find alternative proofs of the congruences for 10- and 20-regular partitions which were proved earlier by Carlson and Webb (Ramanujan J 33:329–337, 2014) by using the theory of modular forms. We use certain p-dissections of
$$(q;q)_{\infty }$$
,
$$\psi (q)$$
,
$$(q;q)_{\infty }^3$$
and
$$\psi (q^2)(q;q)_{\infty }^2$$
.