39 citations · 83 across the 24 of their papers we have counts for
8 papers · 1 filter
The powers of two as sums over partitions
Mircea Merca
In this paper, we investigate two methods to express the natural powers of as sums over integer partitions. First we consider a formula by N. J. Fine that allows us to express…
On a nonlinear relation for computing the overpartition function
Mircea Merca
In 1939, H. S. Zuckerman provided a Hardy-Ramanujan-Rademacher-type convergent series that can be used to compute an isolated value of the overpartition function .…
Rank partition functions and truncated theta identities
Mircea Merca
In , Freeman Dyson defined the concept of rank of an integer partition and introduced without definition the term of crank of an integer partition. A definition for the crank…
Truncated theta series and partitions into distinct parts
Mircea Merca
Linear inequalities involving Euler's partition function have been the subject of recent studies. In this article, we consider the partition function counting the par…
-Series congruences involving statistical mechanics partition functions in regime III and IV of Baxter's solution of the hard-hexagon model
Mircea Merca
For each , the generating function of , the number of partitions of into odd parts or congruent to , , arises naturally in regime III o…
Combinatorial interpretations of two identities of Guo and Yang
Mircea Merca
The restricted partitions in which the largest part is less than or equal to and the number of parts is less than or equal to were investigated by Andrews in \cite{Andrews7…