Related papers: Update on Sidon-Ramsey numbers
We construct a new family of $K_s$-free graphs that leads to improved lower bounds for Ramsey numbers across a wide range of parameters. For any fixed $s \ge 4$, we show that the off-diagonal Ramsey numbers satisfy $r(s, k) \ge k^{s-2 +…
This note reports on the number of s-partitions of a natural number n. In an s-partition each cell has the form $2^k-1$ for some integer k. Such partitions have potential applications in cryptography, specifically in distributed…
A description of solutions of some integral equations has been obtained. A two-radii theorem is obtained as well.
This paper is a complement to our previous paper [21]. It surveys the works on the Furstenberg set $S=\{2^{m}3^{n}: n\ge 0, m\ge 0\}$ and its random version $T$. We also present some new results. For example, it is proved that $T$ almost…
This article summarizes several analyses I discussed at Moriond and I attempt to maintain my speaking voice throughout. I extract several broad themes in the recent development of QCD,and emphasize how the latest results on jet physics…
We introduce the class of supra-SIM sets of natural numbers. We prove that this class is partition regular and closed under finite-embeddability. We also prove some results on sumsets and SIM sets motivated by their positive Banach density…
I briefly discuss some recent developments (and recall some old news) in the theory and phenomenology of generalised parton distributions.
The Raney numbers $R_{p,r}(k)$ are a two-parameter generalization of the Catalan numbers. In this paper, we obtain a recurrence relation for the Raney numbers which is a generalization of the recurrence relation for the Catalan numbers.…
We derive an identity involving Horadam numbers. Numerous new identities as well as those found in the existing literature are subsumed in this single identity.
Many authors have recently studied the degenerate harmonic numbers. This paper makes two main contributions. First, we derive several explicit expressions for these numbers, which are a degenerate version of the ordinary harmonic numbers.…
We give a polynomial improvement to the cycle-complete Ramsey numbers \[ r(C_{\ell},K_k) \geq k^{1+1/(\ell- 2) + \varepsilon_{\ell} + o(1)}, \] for all fixed odd $\ell > 7$ with $k \rightarrow \infty$, for some $\varepsilon_{\ell} > 0$.
We present a partial survey on normal numbers, including Keane's contributions, and with recent developments in different directions.
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
We collect a number of open questions concerning Diophantine equations, Diophantine Approximation and transcendental numbers. Revised version: corrected typos and added references.
In a series of papers the first author and Ono connected the rank, a partition statistic introduced by Dyson, to weak Maass forms, a new class of functions which are related to modular forms. Naturally it is of wide interest to find other…
This work is a survey on completely regular codes. Known properties, relations with other combinatorial structures and constructions are stated. The existence problem is also discussed and known results for some particular cases are…
We use a recent advance in birational geometry to prove new lower bounds on the essential dimension of some finite groups.
We introduce the list colouring extension of classical Ramsey numbers. We investigate when the two Ramsey numbers are equal, and in general, how far apart they can be from each other. We find graph sequences where the two are equal and…
We provide a variational derivation of the limit shape of minimal difference partitions and discuss the link with exclusion statistics. Also see arXiv:0707.2312 for a related paper.
A brief review of large-N_c QCD and the 1/N_c expansion is given. Important results for large-N_c mesons and baryons are highlighted.