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On Euler's Theorem
George E. Andrews, Rahul Kumar, Ae Ja Yee
Euler's theorem asserts that where is the number of partitions of into distinct parts and is the number of partitions of into odd parts. In this p…
math.CO2025
Rank, two-color partitions and Mock theta function
George E. Andrews, Rahul Kumar
In this paper, we establish that the number of partitions of a natural number with positive odd rank is equal to the number of two-color partitions (red and blue), where the smalle…