A Combinatorial Interpretation of j/n kn\choosen+j

2006/04/21 by David Callan, Callan, David
Computer Science · Engineering · Mathematics · #05A15 #Advanced Mathematical Theories #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems #math.CO #msc:05A15

paper · pdf · doi:10.48550/arxiv.math/0604471

Latex, 7 pages, 5 figures

arxiv created 2006/04/21 · openalex publication_date 2006/04/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The identity j/n kn\choosen+j =(k-1) kn-1\choosen+j-1- kn-1\choosen+j shows that j/n kn\choosen+j is always an integer. Here we give a combinatorial interpretation of this integer in terms of lattice paths, using a uniformly distributed statistic. In particular, the case j=1,k=2 gives yet another manifestation of the Catalan numbers.

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