On an inclusion-exclusion formula based on the reflection principle
type: Item
instance of: scholarly article
title: On an inclusion-exclusion formula based on the reflection principle
zbMATH Open document ID: 0617.05008
DOI: 10.1016/0012-365X(87)90197-X
published in: Discrete Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The n-candidate ballot problem corresponding to the standard Young tableau has been solved recently by \textit{D. Zeilberger} [Discrete Math. 44, 325-326 (1983; Zbl 0508.05008)] by using the reflection principle. In this paper, a refinement of Zeilberger's approach is provided in which the reflection principle is formulated through the symmetric group and an inclusion-exclusion formula for the counting problem is developed. This approach reveals the nature in which successive applications of the reflection principle work.
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 3999935
zbMATH Keywords: ballot problem
zbMATH Keywords: Young tableau
zbMATH Keywords: reflection principle
zbMATH Keywords: symmetric group
zbMATH Keywords: inclusion-exclusion formula
zbMATH Keywords: counting problem
author: Toshihiro Watanabe
author: S. G. Mohanty
MaRDI profile type: Publication
cites work: Some Aspects of the Random Sequence
cites work: A $k$-Sample Extension of the One-sided Two-Sample Smirnov Test Statistic
cites work: Q3339843
cites work: The Degree Formula for the Skew-Representations of the Symmetric Group
cites work: The Hook Graphs of the Symmetric Group
cites work: A probabilistic proof of a formula for the number of Young tableaux of a given shape
cites work: Q5814388
cites work: Coincidence probabilities
cites work: Q3283895
cites work: Q3903764
cites work: A combinatorial problem
cites work: Q4435456
cites work: Andre's reflection proof generalized to the many-candidate ballot problem
description: scientific article; zbMATH DE number 3999935