The vertex operator for a generalization of MacMahon’s formula

We provide a vertex operator realization for a two-parameter generalization of MacMahon’s formula introduced by M. Vuletić [Trans. Amer. Math. Soc. 361, 2789 (2009)]. Since the generalized MacMahon function is the kernel function of some Macdonald symmetric function, we consider the action of two vertex operators on a state corresponding to a Macdonald symmetric function. It becomes evident that the vertex operators appear to be the creation and annihilation operators, respectively on the state.