Related papers: Bounds on some edge Folkman numbers

We prove some extensions of Andrews inequality.

We give lower bounds on the case of worst inhomogeneous approximation.

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

We derive upper and lower bounds on the determinant of an exponential matrix. They can be transformed into corresponding bounds for the determinant of a univariate Gaussian matrix.

We give an asymptotic formula for the number of elliptic curves over $\mathbb{Q}$ with bounded Faltings height. Silverman has shown that the Faltings height for elliptic curves over number fields can be expressed in terms of modular…

An approach to constructing an upper bound for the Riemann-Farey sum is described.

In this paper we study the number of finite topologies on an $n$-element set subject to various restrictions.

We improve an existing result on exponential quadrilinear sums in the case of sums over multiplicative subgroups of a finite field and use it to give a new bound on exponential sums with quadrinomials.

We use an old elementary arithmetic argument to find new upper and lower bounds for Sylvester's denumerant function. These bounds are tight enough to get the asymptotic behavior of the denumerant.

In the paper we prove a new upper bound for Heilbronn's exponential sum and obtain some applications of our result to distribution of Fermat quotients.

After a brief review of integrability, first in the absence and then in the presence of a boundary, I outline the construction of actions for the N=1 and N=2 boundary sine-Gordon models. The key point is to introduce Fermionic boundary…

We study the a-numbers and p-ranks of Kummer covers of the projective line, and we give bounds for these numbers.

A surface with boundary is randomly generated by gluing polygons along some of their sides. We show that its genus and number of boundary components asymptotically follow a bivariate normal distribution.

In a given hypercube, draw grid lines parallel to the edges, and consider all hypercuboids (or hypercubes) whose edges are lying on the grid lines or the boundary. We find the limit of the value of the ratio of the arithmetic mean of the…

We obtain some new inequalities of Chebyshev Type.

In this article, we survey the recent results on the Castelnuovo-Mumford regularity of binomial edge ideals and generalized binomial edge ideals. We also generalize some of the known upper bounds for binomial edge ideals to the case of…

We prove a tight lower bound on the Betti numbers of tree and forest ideals and a tight upper bound on certain graded Betti numbers of squarefree monomial ideals.

We prove some sharp extremal distance results for functions in weighted Bergman spaces on the upper halfplane.We also prove such results in the context of bounded strictly pseudoconvex domains with smooth boundary

Examples for bounded Bose fields in two dimensions are presented.

We estimate, in a number field, the number of elements and the maximal number of linearly independent elements, with prescribed bounds on their valuations. As a by-product, we obtain new bounds for the successive minima of ideal lattices.…