CDAM: Computational, Discrete and Applicable Mathematics@LSE

 CDAM Research Report, LSE-CDAM-2009-07

May 2009

Kingman, category and combinatorics

N. H. Bingham and A. J. Ostaszewski 

Kingman's Theorem on skeleton limits - passing from limits as n→∞ along nh (n ∈ ℕ) for enough h>0 to limits as t→∞ for t ∈ ℝ - is generalized to a Baire/measurable setting via a topological approach. Its affinity with a combinatorial theorem due to Kestelman and to Borwein and Ditor and another due to Bergelson, Hindman and Weiss is established. As applications, a theory of ‘rational’ skeletons akin to Kingman's integer skeletons, and more appropriate to a measurable setting, is developed, and two combinatorial results in the spirit of van der Waerden's celebrated theorem on arithmetic progressions are offered.

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