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2016•arXiv (Cornell University)Open access

Computationally Efficient Bounds for the Sum of Catalan Numbers

Kevin Topley

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Abstract

Easily computable lower and upper bounds are found for the sum of Catalan numbers. The lower bound is proven to be tighter than the upper bound, which previously was declared to be only an asymptotic. The average of these bounds is proven to be also an upper bound, and empirically it is shown that the average is superior to the previous upper bound by a factor greater than (9/2).

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What this paper is about

Easily computable lower and upper bounds are found for the sum of Catalan numbers. The lower bound is proven to be tighter than the upper bound, which previously was declared to be only an asymptotic. The average of these bounds is proven to be also an upper bound, and empirically it is shown that the average is superior to the previous upper bound by a factor greater than (9/2).

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Available abstract

Easily computable lower and upper bounds are found for the sum of Catalan numbers. The lower bound is proven to be tighter than the upper bound, which previously was declared to be only an asymptotic. The average of these bounds is proven to be also an upper bound, and empirically it is shown that the average is superior to the previous upper bound by a factor greater than (9/2).

Key concepts: Upper and lower bounds, Catalan, Catalan number, Mathematics, Combinatorics, Mathematical analysis, Philosophy, Humanities

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