The complexity of Euler's integer partition theorem

Authors:
Cristian S. Calude;Elena Calude;Melissa S. Queen
Affiliations:
Department of Computer Science, The University of Auckland, New Zealand;Institute of Information and Mathematical Sciences, Massey University at Auckland, New Zealand;Computer Science Department, Dartmouth College, NH, USA
Venue:
Theoretical Computer Science
Year:
2012

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Abstract

Euler's integer partition theorem, which states that the number of partitions of an integer into odd integers is equal to the number of partitions into distinct integers, ranks 16 in Wells' list of the most beautiful theorems (Wells, 1990) [15]. In this paper, we use the algorithmic method to evaluate the complexity of mathematical statements developed in Calude et al. (2006) [5] and Calude and Calude (2009, 2010) [6,7] and to show that Euler's theorem is in class C"U","3, the same complexity class as the Riemann hypothesis.