Description
Kummer's Theorem says that the highest power of the prime p dividing the binomial coefficient n choose k is the number of carries that occur when adding the base p representations of n and n-k. We've proved an analogous characterization of the highest power of p dividing the number of partitions of [n] into d equal-sized parts. Our motivation comes from certain group-theoretic and number-theoretic problems concerning generation of an alternating group by Sylow subgroups, and I'll discuss applications to such problems.
This is joint work with John Shareshian.
Author
Dr
Russ Woodroofe
(Mississippi State University)
