Journal of Integer Sequences, Vol. 14 (2011), Article 11.1.5

Convex and V-Shaped Sequences of Sums of Functions that Depend on Ceiling Functions

Kabir Rustogi and Vitaly A. Strusevich
School of Computing and Mathematical Sciences
University of Greenwich
Old Royal Naval College
Park Row, Greenwich
London SE10 9LS
United Kingdom


The paper primarily revolves around the convex and V-shaped finite sequences and the inequalities that govern them. We give an elementary proof that a convex sequence is also V-shaped. We prove an inequality that involves an arbitrary nondecreasing function that depends on ceiling functions, thereby establishing the convexity of the corresponding sequence. We present various interpretations and applications of our results, mainly in terms of operations research problems.

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Received October 5 2010; revised version received January 31 2011. Published in Journal of Integer Sequences, February 7 2011.

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