2 papers
math.CO2025
A Refinement of the Crank-Mex Theorem
George E Andrews, Moshe Newman
It is proved that the number of partitions of n with odd mex and k parts that aren't ones equals the number of partitions of n with nonnegative crank and k parts that aren't ones..
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…