2 papers
math.CO2024
Distribution of hooks in self-conjugate partitions
William Craig, Ken Ono, Ajit Singh
We confirm the speculation that the distribution of -hooks among unrestricted integer partitions essentially descends to self-conjugate partitions. Namely, we prove that the num…
math.NT2024
Integer partitions detect the primes
William Craig, Jan-Willem van Ittersum, Ken Ono
We show that integer partitions, the fundamental building blocks in additive number theory, detect prime numbers in an unexpected way. Answering a question of Schneider, we show th…