A multiset hook length formula and some applications

Paul-Olivier Dehaye, Guo-Niu Han

Published 2011-04-28, updated 2011-05-09Version 3

A multiset hook length formula for integer partitions is established by using combinatorial manipulation. As special cases, we rederive three hook length formulas, two of them obtained by Nekrasov-Okounkov, the third one by Iqbal, Nazir, Raza and Saleem, who have made use of the cyclic symmetry of the topological vertex. A multiset hook-content formula is also proved.