Counting and Computing by e
Hassani, Mehdi
Original · EN
In this paper we count the number of paths and cycles in complete graphs by using the number e. Also, we compute the number of derangements in same way. Connection by e yields some nice formulas for the number of derangements, such as Dₙ=!+1/e and Dₙ=(e+e⁻¹)n!- en!, 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.
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