Related papers: Update on Sidon-Ramsey numbers
In this revised version we have improved the treatment of the top and bottom quark mass. This leads to slight changes of the numerical results, especially of those presented in Fig.4. The discussion of the numerical procedure and accuracy…
Recent exact analytical results developed for the random number generators with taps are reported. These results are applicable to a wide class of algorithms, including random walks, cluster algorithms, Ising models. Practical…
A short overview of recent developments on resummations in QCD is presented.
As a result of 33 intercontinental Zoom calls, we characterise big Ramsey degrees of the generic partial order. This is an infinitary extension of the well known fact that finite partial orders endowed with linear extensions form a Ramsey…
We present a refinement of Ramsey numbers by considering graphs with a partial ordering on their vertices. This is a natural extension of the ordered Ramsey numbers. We formalize situations in which we can use arbitrary families of…
I present a brief summary of the most important updates in the MRST determinations of the NLO and NNLO parton distributions. I concentrate on uncertainties due to input assumptions and possible theoretical corrections, particularly isospin…
Two new bounds for multicolor Ramsey numbers are proved: $R(K_3,K_3,C_4,C_4)\geq 27$ and $R_4(C_4)\leq 19$.
The known lower bound for the the classical Ramsey number $R(5,6)$ is improved from $58$ to $59$. The method used to construct the graph is a simple variant of computational methods that have been previously used to construct Ramsey graphs.…
A fan $F_n$ is a graph consisting of $n$ triangles, all having precisely one common vertex. Currently, the best known bounds for the Ramsey number $R(F_n)$ are $9n/2-5 \leq R(F_n) \leq 11n/2+6$, obtained by Chen, Yu and Zhao. We improve the…
The restricted online Ramsey numbers were introduced by Conlon, Fox, Grinshpun and He in 2019. In a recent paper, Briggs and Cox studied the restricted online Ramsey numbers of matchings and determined a general upper bound for them. They…
For a given irrational number, we consider the properties of best rational approximations of given parities. There are three different kinds of rational numbers according to the parity of the numerator and denominator, say odd/odd, even/odd…
We obtain new upper and lower bounds on the number of unit perimeter triangles spanned by points in the plane. We also establish improved bounds in the special case where the point set is a section of the integer grid.
We prove a lemma that is useful to get upper bounds for the number of partitions without a given subsum. From this we can deduce an improved upper bound for the number of sets represented by the (unrestricted or into unequal parts)…
We offer several new summation identities involving harmonic numbers, odd harmonic numbers, and Fibonacci numbers. Our results are derived using three different approaches: partial summation, polynomial identities and binomial…
I survey results about, and recent applications of, Salem numbers.
In this paper, we aim to establish a range of numerical radius inequalities. These discoveries will bring us to a recently validated numerical radius inequality and will present numerical radius inequalities that exhibit enhanced precision…
The aim of this note is to provoke discussion concerning arithmetic properties of function $p_{d}(n)$ counting partitions of an positive integer $n$ into $d$-th powers, where $d\geq 2$. Besides results concerning the asymptotic behavior of…
Our number system is a magnificent tool. But it is far from perfect. Can it be improved? In this paper some possibilities are discussed, including the use of a different base or directed (negative as well as positive) numerals. We also put…
We derive new matrix representation for higher order Daehee numbers and polynomials, the higher order lambda-Daehee numbers and polynomials and the twisted lambda-Daehee numbers and polynomials of order k. This helps us to obtain simple and…
New sets (typically found by computer search) with Sidon constant equal to the square root of their cardinalities are given. For each integer $N$ there are only a finite number of groups of prime order containing $N$-element extreme sets.…