A uniformly distributed statistic on a class of lattice paths
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Publication:1773166
zbMATH Open1060.05003arXivmath/0310461MaRDI QIDQ1773166
Author name not available (Why is that?)
Publication date: 25 April 2005
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/math/0310461
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