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A Note on Combinatorial Identities for Partial Sums

Published online by Cambridge University Press:  20 November 2018

S. G. Mohanty
S. G. Mohanty*
Affiliation:
Mcmaster University, Hamilton, Ontario
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For a sequence σ = (x1, …, xn) of real numbers, let σi and respectively denote the cyclic permutation (xi, xi+1, …, xi-1) and the reverse cyclic permutation (xj, xj-1, …, xj+1), and let . Also denote by Mrj(σ) and mrj(σ) the rth largest and the rth smallest numbers respectively, among the first j partial sums s1, s2, …, Sj for 1≤r≤j≤n. As usual, let the superscripts + and — respectively mean maximize and minimize with zero.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 1 , January 1971 , pp. 65 - 67
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Dwass, M., A fluctuation theorem for cyclic random variables, Ann. Math. Statist. 33 (1962), 1450-1454.Google Scholar
2. Graham, R. L., A combinatorial theorem for partial sums, Ann. Math. Statist. 34 (1963), 1600-1602.Google Scholar
3. Harper, L. H., A family of combinatorial identities, Ann. Math. Statist. 37 (1966), 509-512.Google Scholar