منابع مشابه
New Lower Bounds for Heilbronn Numbers
The n-th Heilbronn number, Hn, is the largest value such that n points can be placed in the unit square in such a way that all possible triangles defined by any three of the points have area at least Hn. In this note we establish new bounds for the first Heilbronn numbers. These new values have been found by using a simple implementation of simulated annealing to obtain a first approximation an...
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Let p/q be a rational noninteger number with p > q ≥ 2. A real number λ > 0 is a Zp/q-number if {λ(p/q)n} < 1/q for every nonnegative integer n, where {x} denotes the fractional part of x. We develop several algorithms to search for Zp/q-numbers, and use them to determine lower bounds on such numbers for several p and q. It is shown, for instance, that if there is a Z3/2-number, then it is grea...
متن کاملNew lower bounds for Ramsey numbers of graphs and hypergraphs
Let G be an r-uniform hypergraph. The multicolor Ramsey number rk(G) is the minimum n such that every k-coloring of the edges of the complete r-uniform hypergraph K n yields a monochromatic copy of G. Improving slightly upon results from [1], we prove that tk + 1 ≤ rk(K2,t+1) ≤ tk + k + 2, where the lower bound holds when t and k are both powers of a prime p. When t = 1, we improve the lower bo...
متن کاملNew Lower Bounds for 28 Classical Ramsey Numbers
We establish new lower bounds for 28 classical two and three color Ramsey numbers, and describe the heuristic search procedures used. Several of the new three color bounds are derived from the two color constructions; specifically, we were able to use (5, k)-colorings to obtain new (3, 3, k)-colorings, and (7, k)-colorings to obtain new (3, 4, k)-colorings. Some of the other new constructions i...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2002
ISSN: 1077-8926
DOI: 10.37236/1623