1 research outputs found
Johnson's bijections and their application to counting simultaneous core partitions
Johnson recently proved Armstrong's conjecture which states that the average
size of an -core partition is . He used various
coordinate changes and one-to-one correspondences that are useful for counting
problems about simultaneous core partitions. We give an expression for the
number of -core partitions where
contains at least one pair of relatively prime
numbers. We also evaluate the largest size of a self-conjugate
-core partition