Counting and Computing by E
نویسنده
چکیده
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 = ⌊ n!+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. 2000Mathematics Subject Classification: 40A25, 05C17, 05C38, 65L99, 33B20, 33C20, 26D15, 11J72, 20B40.
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تاریخ انتشار 2006