Polite numbers and length spectra

03/20/2012 - 12:15pm
03/20/2012 - 1:10pm
Wai Yan Pong (California State University Dominguez Hills)

A decomposition of a natural number n of length m is sequence of m consecutive natural numbers whose sum is n. The length spectrum of n is the set of lengths of its decompositions. Two numbers are spectral equivalent if they have the same length spectrum. We show that this equivalence relation is computable and will demonstrate a rather surprising fact about the sizes of the spectral classes. We also talk about how often could one guess a number from its spectrum.

Millikan 208 (Pomona College)