Dimensions of the irreducible representations of the symmetric and   alternating group
  We establish the existence of an irreducible representation of $A_n$ whose dimension does not occur as the dimension of an irreducible representation of $S_n$, and vice versa. This proves a conjecture by Tong-Viet. The main ingredient in the proof is a result on large prime factors in short intervals. 
Korneel Debaene
math.CO