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An inequality related to two integer sequences satisfying an order condition. (English) Zbl 1007.05019

The author considers a nondecreasing sequence \((c,d)\) obtained by merging two disjoint nondecreasing sequences \(c\) and \(d\), which consist of non-negative integers and have the same lengths. The following inequality is formulated: If \((c,d)\) contains \(h+1\) maximal subsequences of \(c\) and \(d\), and the sums of the \(r\)th powers of the members are the same in both \(c\) and \(d\) for \(-1\leq r\leq 1\), then the sum of the \(h\)th powers is greater in the sequence which contains the largest integer of \((c,d)\). The paper includes a skech of a proof of the inequality and briefly describes its application to a computer graphics problem.

MSC:

05A20 Combinatorial inequalities
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
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