3 papers
math.CO2025
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…
math.NT2025
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…
math.CO2025
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…