Arithmetic properties of l-regular partitions and l-regular bipartitions

Abstract

AbstractFor any positive integer l, let $$b_l(n)$$ b l ( n ) and $$B_l(n)$$ B l ( n ) represent the number of l-regular partitions and l-regular bipartitions respectively. By employing q-identities, we prove new congruences for $$b_{11}(n)$$ b 11 ( n ) , $$b_{19}(n)$$ b 19 ( n ) , $$b_{55}(n)$$ b 55 ( n ) , $$B_{11}(n)$$ B 11 ( n ) and $$B_{13}(n)$$ B 13 ( n ) .