CDAM: Computational, Discrete and Applicable Mathematics@LSE | |
CDAM Research Report, LSE-CDAM-2009-07May 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.A PDF file (241 kB) with the full contents of this report can be downloaded by clicking here.
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