On an inclusion-exclusion formula based on the reflection principle
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.
scientific article; zbMATH DE number 3999935