✦ LIBER ✦
On Four Colored Sets with Nondecreasing Diameter and the Erdős–Ginzburg–Ziv Theorem
✍ Scribed by David J. Grynkiewicz
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 197 KB
- Volume
- 100
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
✦ Synopsis
A set X; with a coloring D: X ! Z m ; is zero-sum if P x2X DðxÞ ¼ 0: Let f ðm; rÞ (let f zs ðm; 2rÞ) be the least N such that for every coloring of 1; . . . ; N with r colors (with elements from r disjoint copies of Z m ) there exist monochromatic (zero-sum) m-element subsets B 1 and B 2 ; not necessarily the same color, such that (a)
We show that f zs ðm; 4Þ ¼ f ðm; 4Þ: # 2002 Elsevier Science (USA)