39 citations · 43 across the 10 of their papers we have counts for
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Dyson's crank and unimodal compositions
Cristina Ballantine, Mircea Merca
The crank is a partition statistic requested by Dyson in 1944 in order to combinatorially prove a Ramanujan congruence of Euler's partition function . In this paper, we provi…
Overpartitions and functions from multiplicative number theory
Mircea Merca
Let and be two nonnegative integers such that . For an arbitrary sequence of complex numbers, we consider the generalized Lambert series in o…
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…
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…
On the partitions into distinct parts and odd parts
Mircea Merca
In this paper, we show that the difference between the number of parts in the odd partitions of and the number of parts in the distinct partitions of satisfies Euler's recu…