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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★ 1 cited
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…