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A New Identity and Some Applications

Published online by Cambridge University Press:  20 November 2018

W. O. J. Moser  and
Richard Pollack
W. O. J. Moser
Affiliation:
Department of Mathematics Burnside Hall Mcgill University, Montreal, Que H3A2K6
Richard Pollack
Affiliation:
McGill University, New York University, Courant Institute of Mathematical Sciences
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Abstract

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Let (n|k) denote the number of k-choices 1≤x1<x2<…<xk≤n satisfying xi-xi-1≥2, i = 2,…, k, n + x1-xk≥2; let (m, n | k) = Σi+j=k (m | i)(n | j). Several elementary proofs of the new identity (m, n|k) = (m + n | k) if 0≤k<m≤n. and

if 0≤m≤n, m≤k, are given. Generalizations and applications are considered.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 3 , 01 September 1980 , pp. 281 - 290
Copyright
Copyright © Canadian Mathematical Society 1980

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