Asymptotics of the number of standard Young tableaux of skew shape
  We give new bounds and asymptotic estimates on the number of standard Young tableaux of skew shape in a variety of special cases. Our approach is based on Naruse's hook-length formula. We also compare our bounds with the existing bounds on the numbers of linear extensions of the corresponding posets. 
Alejandro Morales, Igor Pak, Greta Panova
math.CO