A Combinatorial Interpretation of j/n {kn}\choose{n+j}

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dc.creatorCallan, David
dc.date2006-04-21
dc.date.accessioned2026-07-07T07:11:10Z
dc.date.available2026-07-07T07:11:10Z
dc.descriptionThe identity j/n {kn}\choose{n+j} =(k-1) {kn-1}\choose{n+j-1}- {kn-1}\choose{n+j} shows that j/n {kn}\choose{n+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.
dc.descriptionLatex, 7 pages, 5 figures
dc.identifierhttps://arxiv.org/abs/math/0604471
dc.identifierhttp://arxiv.org/abs/math/0604471
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/111653
dc.subjectCombinatorics
dc.subject05A15
dc.titleA Combinatorial Interpretation of j/n {kn}\choose{n+j}
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