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Ramsey Functions for Quasi-Progressions

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Abstract.

 A quasi-progression of diameter n is a finite sequence for which there exists a positive integer L such that for . Let be the least positive integer such that every 2-coloring of will contain a monochromatic k-term quasi-progression of diameter n. We give a lower bound for in terms of k and i that holds for all . Upper bounds are obtained for in all cases for which . In particular, we show that . Exact formulae are found for and . We include a table of computer-generated values of , and make several conjectures.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of North Carolina at Greensboro, NC 27412, USA, , , , , , US

    Bruce M. Landman

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  1. Bruce M. Landman
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Received: September 22, 1995 / Revised: February 28, 1997

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Landman, B. Ramsey Functions for Quasi-Progressions. Graphs Comb 14, 131–142 (1998). https://doi.org/10.1007/s003730050021

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  • DOI: https://doi.org/10.1007/s003730050021

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