Related papers: Update on Sidon-Ramsey numbers

We highlight a certain compactness of Sidon sets and $B_2[g]$-sets and provide several applications. Notably, we prove the existence of such sets that maximize certain functions. In particular, we show the existence of a Sidon set whose…

In this paper, we present an improved continued fraction approximation of the Wallis ratio. This approximation is fast in comparison with the recently discovered asymptotic series. We also establish the double-side inequality related to…

We introduce and study a new kind of congruent number problem on the right trapezoid.

We survey recent developments on the Restriction conjecture.

We extend recent results by G. E. Andrews and G. Simay on the $m$th largest and $m$th smallest parts of a partition to the more general context of skew plane partitions. In order to do this, we introduce new objects called skew plane…

We introduce several statistics on ordered partitions of sets, that is, set partitions where the blocks are permuted arbitrarily. The distribution of these statistics is closely related to the q-Stirling numbers of the second kind. Some of…

We give asymptotic sharp estimates for the cardinality of a set of residue classes with the property that the representation function is bounded by a prescribed number. We then use this to obtain an analogous result for sets of integers,…

In this note we give an overview of some of our recent work on Anosov representations of discrete groups into higher rank semisimple Lie groups.

We derive new matrix representation for higher-order changhee numbers and polynomials. This helps us to obtain simple and short proofs of many previous results on higher-order changhee numbers and polynomials. Moreover, we obtain recurrence…

We establish some bounds on the number of higher-dimensional partitions by volume. In particular, we give bounds via vector partitions and MacMahon's numbers.

In the revised version of the paper, we correct misprints and add some new statements.

We establish new lower bounds for $28$ classical two and three color Ramsey numbers, and describe the heuristic search procedures we used. Several of the new three color bounds are derived from the two color constructions; specifically, we…

Using computational techniques we derive six new upper bounds on the classical two-color Ramsey numbers: R(3,10) <= 42, R(3,11) <= 50, R(3,13) <= 68, R(3,14) <= 77, R(3,15) <= 87, and R(3,16) <= 98. All of them are improvements by one over…

We introduce the notion of Ramsey partition regularity, a generalisation of partition regularity involving infinitary configurations. We provide characterisations of this notion in terms of certain ultrafilters related to tensor products…

Circulant graphs have been used to effectively establish lower bounds on many classical Ramsey numbers. Here, we construct circulant graphs of prime order that sharpen the best published lower bounds on two Ramsey numbers. Generalizing…

We present some new lower bound estimates for certain numbers in Laver table theory and introduce several related structures of interest.

I discuss the current status of parton distributions. I outline the wide variety of different parton distributions available, and highlight which are either necessary or suitable for use at present.

New cases of the multiplicity conjecture are considered.

We prove a Ramsey theorem for finite sets equipped with a partial order and a fixed number of linear orders extending the partial order. This is a common generalization of two recent Ramsey theorems due to Soki\'c. As a bonus, our proof…

By some new recursive algorithms, in this paper, we will give some improvements on Waring's problem.