39 citations · 83 across the 24 of their papers we have counts for
32 papers
Dyadic Structure of the Two-Block Odd Partition Function and Theta-Weighted Congruences for
Mircea Merca
The two-block odd partition function \(a(n)\) is the signed enumeration of partitions into exactly two distinct part sizes, each occurring an odd number of times. By separating the…
The two-block odd partition function
Mircea Merca
We investigate arithmetic and combinatorial properties of the function , which is the signed number of partitions of into exactly two distinct part sizes, each occurring…
MacMahon-type -series
Mircea Merca
Motivated by earlier work of P.~A.~MacMahon and recent contributions of T.~Amdeberhan, G.~E.~Andrews, K.~Ono, A.~Singh, and R.~Tauraso on higher-order partition enumerants, we stud…
From crank to congruences
Tewodros Amdeberhan, Mircea Merca
In this paper, we investigate the arithmetic properties of the difference between the number of partitions of a positive integer with even crank and those with odd crank, denot…
Do perfect powers repel partition numbers?
Mircea Merca, Ken Ono, Wei-Lun Tsai
In 2013 Zhi-Wei Sun conjectured that is never a power of an integer when We confirm this claim in many cases. We also observe that integral powers appear to repel the…
Elementary symmetric partitions
Cristina Ballantine, George Beck, Mircea Merca +1
Let e_k(x_1,...,x_l) be an elementary symmetric polynomial and let mu = (mu_1,...,mu_l) be an integer partition. Define pre_k(mu) to be the partition whose parts are the summands i…