Dominance Theory and Plane Partitions:Ⅰ.Introduction

Let λ∈Nsatisfying λλ…λfor natural number set N. An orderideal λ determined by λ is defined to be {（i,j）:1jλ,1ik}N. A planepartition （reverse） π of shape λ is an order- reversing （preserving） map from λto N-0. If P is any set of plane partitions, the generating function （abbrev.asGF） of P is the polynomial or fromal power series , where |π|denotethe weight of π. The enumeration theory of plane partitions is an active fieldof combinatorics. There are several approaches which have been successfully