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math.NT2021
A crank-based approach to the theory of 3-core partitions
Olivier Brunat, Rishi Nath
This note is concerned with the set of integral solutions of the equation , where is a positive integer. We will describe a parametrization of this set using th…
math.NT2012
The number of self-conjugate core partitions
Christopher R. H. Hanusa, Rishi Nath
A conjecture on the monotonicity of t-core partitions in an article of Stanton [Open positivity conjectures for integer partitions, Trends Math., 2:19-25, 1999] has been the cataly…