Ramanujan’s congruences
for the unrestricted partition function p(n) with 5, 7 and 11 as moduli can be shown
to be equivalent to precisely similar congruences for some restricted partition
functions of the type
(1)
where to determine the value of (1) we count all the unrestricted partitions of n
excepting those which contain any number of the forms tn or tn ± r as a
part. The purpose of the present paper is to deal with congruences modulo
11.
