Rahul Kumar

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20242026

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math.CO2025

On Euler's Theorem

George E. Andrews, Rahul Kumar, Ae Ja Yee

Euler's theorem asserts that $A (n) = B (n)$ where $A (n)$ is the number of partitions of $n$ into distinct parts and $B (n)$ is the number of partitions of $n$ 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…