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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


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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

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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

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## 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