Partition properties of the dense local order and a colored version of Milliken’s theorem

Abstract

We study finite dimensional partition properties of the countable homogeneous dense local order (a directed graph closely related to the order structure of the rationals). Some of our results use ideas borrowed from the partition calculus of the rationals and are obtained thanks to a strengthening of Milliken’s theorem on trees.

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Correspondence to Claude Laflamme.

Additional information

C. Laflamme was supported by NSERC of Canada Grant # 690404.

L. Nguyen Van Thé would like to thank the support of the Department of Mathematics & Statistics Postdoctoral Program at the University of Calgary.

N. W. Sauer was supported by NSERC of Canada Grant # 691325.

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Laflamme, C., Van Thé, L.N. & Sauer, N.W. Partition properties of the dense local order and a colored version of Milliken’s theorem. Combinatorica 30, 83–104 (2010). https://doi.org/10.1007/s00493-010-2445-y

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Mathematics Subject Classification (2000)

  • 03E02
  • 05C55
  • 05D10