COUNTING PATHS IN YOUNG LATTICE

被引：12
|
作者：
GESSEL, IM [1 ]
机构：
[1] BRANDEIS UNIV,DEPT MATH,WALTHAM,MA 02254
来源：
JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 1993年 / 34卷 / 01期
基金：
美国国家科学基金会;
关键词：
YOUNG LATTICE; TABLEAUX; OSCILLATING TABLEAUX; SYMMETRICAL FUNCTIONS; SCHUR FUNCTIONS; PIERIS RULE; DIFFERENTIAL POSETS;
D O I：
10.1016/0378-3758(93)90038-8
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
Young's lattice is the lattice of partitions of integers, ordered by inclusion of diagrams. Standard young tableaux can be represented as paths in Young's lattice that go up by one square at each step, and more general paths in Young's lattice correspond to more general kinds of tableaux. Using the theory of symmetric functions, in particular Pieri's rule for multiplying a Schur function by a complete symmetric function, we derive formulas for counting paths in Young's lattice that go up or down by horizontal or vertical strips. Our results are related to Richard Stanley's theory of differential posets in the special case of Young's lattice.
引用
收藏
页码：125 / 134
页数：10
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