Related papers: Update on Sidon-Ramsey numbers
We improve the previuosly known bound for some vertex Folkman numbers.
We give a simple proof of the recent remarkable exponential improvement for Ramsey lower bounds, obtained by Ma, Shen and Xie. Our key ingredient is an alternative construction based on Gaussian random graphs, which allows us to simplify…
We estimate the error term in the asymptotic formula of the Sidon constant for (ordinary) Dirichlet polynomials by providing explicit lower and upper bounds. The lower bound is already implicitly known, but we supply the necessary…
We establish the existence of generalised Sidon sets enjoying additional Ramsey-type properties, which are motivated by questions of Erd\H{o}s and Newman and of Alon and Erd\H{o}s.
Sidon spaces have been introduced by Bachoc, Serra and Z\'emor in 2017 as the $q$-analogue of Sidon sets. The interest on Sidon spaces has increased quickly, especially after the work of Roth, Raviv and Tamo in 2018, in which they…
In this paper we study a sequence involving the prime numbers by deriving two asymptotic formulas and finding new upper and lower bounds, which improve the currently known estimates.
Using cyclic graphs I give new lower bounds for two color and multicolor Ramsey numbers: R(4,16)>163, R(5,11)>170, R(5,12)>190, R(5,13)>212, R(5,14)>238, R(3,3,9)>117, R(3,3,10)>141 and R(3,3,11)>157. Improving the previous best known…
We present new bounds for the Berezin number inequalities which improve on the existing bounds. We also obtain bounds for the Berezin norm of operators as well as the sum of two operators.
We give a coding based perspective, on a result of Erd\'{o}s, on a lower bound for the diagonal ramsey numbers.
We estimate Ramsey numbers for bipartite graphs with small bandwidth and bounded maximum degree. In particular we determine asymptotically the two and three color Ramsey numbers for grid graphs. More generally, we determine asymptotically…
The lower bound for the classical Ramsey number R(4, 8) is improved from 56 to 58. The author has found a new edge coloring of K_{57} that has no complete graphs of order 4 in the first color, and no complete graphs of order 8 in the second…
We obtain a small improvement of Gallagher's larger sieve and we extend it to higher dimensions. We also obtain two interesting upper bounds for the number of solutions to polynomial congruences.
We discuss the latest update of the MRST parton distributions in response to the most recent data. We discuss the areas where there are hints of difficulties in the global fit, and compare to some other updated sets of parton distributions,…
We use finite fields and extend a result of Fan Chung to give eight new, nontrivial, lower bounds.
Two new generalized Fibonacci number summation identities are stated and proved, and two other new generalized Fibonacci number summation identities are derived from these, of which two special cases are already known in literature.
We introduce and study expansions of real numbers with respect to two integer bases.
We show that any graded digraph $D$ on $n$ vertices with maximum degree $\Delta$ has an oriented Ramsey number of at most $C^\Delta n$ for some absolute constant $C > 1$, improving upon a recent result of Fox, He, and Wigderson. In…
Since 2002, the best known upper bound on the Ramsey numbers R n (3) = R(3,. .. , 3) is R n (3) $\le$ n!(e -- 1/6) + 1 for all n $\ge$ 4. It is based on the current estimate R 4 (3) $\le$ 62. We show here how any closing-in on R 4 (3)…
This article highlights historical achievements in the partition theory of countable homogeneous relational structures, and presents recent work, current trends, and open problems. Exciting recent developments include new methods involving…
The basic result of this note is a statement about the existence of families of partitions of the set of natural numbers with some favourable properties, the n-optimal matrices of partitions. We use this to improve a decomposition result…