A uniformly distributed parameter on a class of lattice paths

2003/10/29 by David Callan, Callan, David
Computer Science · Mathematics · #05A15 #Advanced Combinatorial Mathematics #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #math.CO #msc:05A15

paper · pdf · doi:10.48550/arxiv.math/0310461

LateX 8 pages

arxiv created 2003/10/29 · openalex publication_date 2003/10/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G_n denote the set of lattice paths from (0,0) to (n,n) with steps of the form (i,j) where i and j are nonnegative integers, not both 0. Let D_n denote the set of paths in G_n with steps restricted to (1,0), (0,1), (1,1), so-called Delannoy paths. Stanley has shown that | G_n | = 2^(n-1) | D_n | and Sulanke has given a bijective proof. Here we give a simple parameter on G_n that is uniformly distributed over the 2^(n-1) subsets of [n-1] = 1,2,...,n-1 and takes the value [n-1] precisely on the Delannoy paths.

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