Increasing Consecutive Patterns in Words

By Mingjia Yang and Doron Zeilberger


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[J. of Algebraic Combinatorics, published on-line before print. Volume and page tbd]

First Written: May 15, 2018; This version: Sept. 28, 2018.


Let r be a positive integer. In how many ways can you place, in a line, n different people , all of different heights, such that you will not have a situation where there are r consecutive people with increasing height? The answers are