Ramsey Functions for Quasi-Progressions |
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Authors: | Bruce M Landman |
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Institution: | (1) Department of Mathematical Sciences, University of North Carolina at Greensboro, NC 27412, USA, US |
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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.
Received: September 22, 1995 / Revised: February 28, 1997 |
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