Journal article
Pseudo-arithmetic sets and Ramsey theory
Journal of combinatorial theory. Series A, Vol.106(1), pp.49-57
2004
DOI: 10.1016/j.jcta.2004.01.002
Abstract
Given a set A of natural numbers, let d(A)={(y−x) | x<y∈A} and let m( A)=min( d( A)). The set A is said to be pseudo-arithmetic if m(A) | (x−y) for all x, y∈ A. We prove a pseudo-arithmetic Ramsey theorem: for any c, k, n>0 there is a number p= P( n; c, k), so that for any c-coloring f : [p] k→[c] , there is a pseudo-arithmetic set A with | A|= n and f constant on [ A] k . We prove that P(3;2,2)=13, and show that P(3,3,2)⩾614. We prove a divisible Schur theorem: for any c>0 there is a number s= S d ( c), so that for any c-coloring χ:[ s]→[ c], there is a monochromatic set { x, y, x+ y} with x | y .
Details
- Title: Subtitle
- Pseudo-arithmetic sets and Ramsey theory
- Creators
- Peter Floodstrand Blanchard - University of Iowa, Mathematics
- Resource Type
- Journal article
- Publication Details
- Journal of combinatorial theory. Series A, Vol.106(1), pp.49-57
- DOI
- 10.1016/j.jcta.2004.01.002
- ISSN
- 0097-3165
- eISSN
- 1096-0899
- Publisher
- Elsevier Inc
- Language
- English
- Date published
- 2004
- Academic Unit
- Mathematics
- Record Identifier
- 9983985885002771
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