Congruences involving generalized Frobenius partitions.
Cranks and t-cores.
Distribution of the partition function modulo .
Elementary Proofs in the Theory of Partitions.
Enumeration of the partitions of an integer into parts of a specified number of different sizes and especially two sizes.
Even partition functions.
Exceptional congruences for powers of the partition function
Exotic Bailey-Slater spt-functions III: Bailey pairs from groups B, F, G, and J
We continue to investigate spt-type functions that arise from Bailey pairs. In this third paper on the subject, we proceed to introduce additional spt-type functions. We prove simple Ramanujan type congruences for these functions which can be explained by an spt-crank-type function. The spt-crank-type functions are actually defined first, with the spt-type functions coming from setting z = 1 in this definition. We find some of the spt-crank-type functions to have interesting representations as single...
Generalization of Ramanujan's Congruences p(5m+4) ...O (mod 5) and p(7m+5) ...0 (mod 7).
Generalizations and refinements of a partition theorem of Göllnitz.
Generalizations of Dyson's rank and non-Rogers-Ramanujan partitions.
Infinite families of divisibility properties modulo 4 for non-squashing partitions into distinct parts.
Linear congruences and a conjecture of Bibak
We address three questions posed by K. Bibak (2020), and generalize some results of K. Bibak, D. N. Lehmer and K. G. Ramanathan on solutions of linear congruences . In particular, we obtain explicit expressions for the number of solutions, where ’s are squares modulo . In addition, we obtain expressions for the number of solutions with order restrictions or with strict order restrictions in some special cases. In these results, the expressions for the number of solutions involve Ramanujan...
Lucas partitions.
MacMahon's partition analysis XI: Broken diamonds and modular forms
New infinite families of Ramanujan-type congruences modulo 9 for overpartition pairs
Let denote the number of overpartition pairs of n. Bringmann and Lovejoy (2008) proved that for n ≥ 0, . They also proved that there are infinitely many Ramanujan-type congruences modulo every power of odd primes for . Recently, Chen and Lin (2012) established some Ramanujan-type identities and explicit congruences for . Furthermore, they also constructed infinite families of congruences for modulo 3 and 5, and two congruence relations modulo 9. In this paper, we prove several new infinite...
New properties for the Ramanujan-Göllnitz-Gordon continued fraction
Observations on the parity of the total number of parts in odd--part partitions.
On a conjecture of Andrews.
On a partition theorem of Göllnitz.