Abstract
Ramsey numbers similar to those of van der Waerden are examined. Rather than considering arithmetic sequences, we look at increasing sequences of positive integers {x1,x2,...,xn} for which there exists a polynomial {cauchy integral}(x)=∑ri=0aix i, with aiε{lunate}Z and xj+1={cauchy integral}(xj). We denote by pr(n) the least positive integer such that if [1,2,...,pr(n)] is 2-colored, then there exists a monochromatic sequence of length n generated by a polynomial of degree ≤r. We give values for pr(n) for n≤5, as well as lower bounds for p1(n) and p2(n). We also give an upper bound for certain Ramsey numbers that are in between pn-2(n) and the nth van der Waerden number.
Original language | English (US) |
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Pages (from-to) | 77-83 |
Number of pages | 7 |
Journal | Discrete Mathematics |
Volume | 68 |
Issue number | 1 |
DOIs | |
State | Published - 1988 |
Externally published | Yes |
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics