On a restricted type of partitions into parts divisible by the least part
On congruence properties of the partition function.
On multiperiodic infinite recursions and their finite core.
On partitions with difference conditions.
On powers of 2 dividing the values of certain plane partition functions.
On primitive 3-smooth partitions of .
On the asymptotics of the number of p̅-core partitions of integers
On the existence of a non-zero lower bound for the number of Goldbach partitions of an even integer.
On the number of representations of integers as the sum of k terms
On the parity of generalized partition functions, III
Improving on some results of J.-L. Nicolas [15], the elements of the set , for which the partition function (i.e. the number of partitions of with parts in ) is even for all are determined. An asymptotic estimate to the counting function of this set is also given.
On the parity of the number of multiplicative partitions
Parity indices of partitions
Parity of the partition function.
Parity results for broken k-diamond partitions and (2k+1)-cores
Proof of a conjecture of Hirschhorn and Sellers on overpartitions
Let p̅(n) denote the number of overpartitions of n. It was conjectured by Hirschhorn and Sellers that p̅(40n+35) ≡ 0 (mod 40) for n ≥ 0. Employing 2-dissection formulas of theta functions due to Ramanujan, and Hirschhorn and Sellers, we obtain a generating function for p̅(40n+35) modulo 5. Using the (p, k)-parametrization of theta functions given by Alaca, Alaca and Williams, we prove the congruence p̅(40n+35) ≡ 0 (mod 5) for n ≥ 0. Combining this congruence and the congruence p̅(4n+3) ≡ 0 (mod...
-analogue of a binomial coefficient congruence.
-series, elliptic curves, and odd values of the partition function.
q-Identities for Maass waveforms (Corrigendum).
Quadratic forms and four partition functions modulo 3.
Quintuple products and Ramanujan's partition congruence p(11n+6) ≡ 0(mod 11)