Some Unexpected Connections Between Analysis and Combinatorics

Dorin Andrica () and Eugen J. Ionascu ()
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Dorin Andrica: Babeş-Bolyai University, Faculty of Mathematics and Computer Science
Eugen J. Ionascu: Columbus State University, Math Department

A chapter in Mathematics Without Boundaries, 2014, pp 1-19 from Springer

Abstract: Abstract We go through a series of results related to the k-signum equation $\pm 1^k\pm 2^k\pm\cdots\pm n^k=0$ . We are investigating the number S k (n) of possible writings and the asymptotic behavior of these numbers, as k is fixed and $n\to \infty$ . The results are presented in connections with the Erdös–Surányi sequences. Analytic methods and algebraic ones are employed in order to predict the asymptotic behavior in general and to study in detail various situations for small values of k. Some simplifications and further ramifications are discussed in the end about the recent proof of Andrica–Tomescu conjecture.

Keywords: Derivative; Partition of integers; Asymptotic formula; Integral representation; Random variable; Erdös–Surányi sequence (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4939-1106-6_1

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DOI: 10.1007/978-1-4939-1106-6_1

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