Counting and Computing by e

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Hassani, Mehdi (2005) Counting and Computing by e. Research report collection, 8 (1).


In this research and review paper, using some inequalities and relations involving e, we count the number of paths and cycles in complete graphs the number of derangements. Connection by e yields some nice formulas for the number of derangements, and using these relations allow us to compute some incomplete gamma functions and hypergeometric summations; these connections are hidden in the heart of a nice polynomial that we call it derangement function and a simple ordinary differential equation concerning it.

Item type Article
Subjects Historical > FOR Classification > 0101 Pure Mathematics
Historical > FOR Classification > 0102 Applied Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords approximation, complete graphs, cycles, derangements, derangement function, differential equation, e, incomplete gamma function, hypergeometric function, inequality, irrational number, paths, permutation
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