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 neces
Monochromatic and zero-sum sets of nondecreasing diameter
✍ Scribed by Arie Bialostocki; Paul Erdös; Hanno Lefmann
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 721 KB
- Volume
- 137
- Category
- Article
- ISSN
- 0012-365X
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📜 SIMILAR VOLUMES
A main result proved in this paper is the following. Theorem. Let G be a noncomplete graph on n vertices with degree sequence where R is the zero-sum Ramsey number.
We study quadratic residue difference sets, GMW difference sets, and difference sets arising from monomial hyperovals, all of which are (2 d &1, 2 d&1 &1, 2 d&2 &1) cyclic difference sets in the multiplicative group of the finite field F 2 d of 2 d elements, with d 2. We show that, except for a few
## Abstract We prove the following generalization of earlier results of Bialostocki and Dierker [3] and Caro [7]. Theorem. Let __t__ ⩾ __k__ ⩾ 2 be positive integers such that __k__ | __t__, and let __c :E__(K) → ℤ~__k__~ be a mapping of all the __r__‐subsets of an __rt__ + __k__ −1 element set in