Some congruences for e-regular partitions with certain restrictions
Some congruences for e-regular partitions with certain restrictions
Blog Article
Let $ {
m{pod}}_ell(n) $ and $ {
m{ped}}_ell(n) $ denote the number of $ ell $-regular partitions of a positive integer $ n $ into distinct odd parts and the number of $ ell $-regular partitions of a positive integer Bocce $ n $ into distinct even parts, respectively.Our first goal in this note was to prove two congruence relations for $ {
m{pod}}_ell(n) $.Furthermore, we found a formula for the action of the Hecke operator on a class of eta-quotients.
As two applications of this result, we obtained two infinite families of congruence relations for $ {
m pod}_5(n) $.We also proved a congruence relation for $ {
m{ped}}_ell(n) $.In particular, we established a congruence relation modulo 2 connecting $ Toy Tools {
m{pod}}_ell(n) $ and $ {
m{ped}}_ell(n) $.