平面分拆的矢量控制方法——列严格梯形平面分拆<英文>

Dominance Method for Plane Partitions——Column-Strict Ladder Plane Partitions

作为移位平面分拆的自然拓广,本文引入了梯形平面分拆的概念.应用矢量控制技巧,建立了给定形状和行(列)分部约束的列严格梯形平面分拆集合之枚举函数的初等对称函数行列式表达式.其中之一的重要特例构成了关于循环对称平面分拆的Macdonald猜想的证明基础.

The concept of ladder plane partition is introduced which may be regarded as a natural extension of the shifted one. By employing the dominance technique, a pair of determinant expressions in terms of symmetric functions, for the generating function of column-strict ladder plane partitions of fixed shape with row and column flags, is established. One of them forms the basis for proving the famous Macdonald's conjecture on cyclically symmetric plane parti tions.