Related papers: New Lower Bound Formulas for Multicolored Ramsey N…
In the paper we present some new inversion formulas and two new formulas for Stirling numbers.
The problem of constructing explicit functions which cannot be approximated by low degree polynomials has been extensively studied in computational complexity, motivated by applications in circuit lower bounds, pseudo-randomness,…
We prove new upper bounds on the multicolour Ramsey numbers of paths and even cycles. It is well known that $(k-1)n+o(n)\leq R_k(P_n)\leq R_k(C_n)\leq kn+o(n)$. The upper bound was recently improved by S\'ark\"ozy who showed that…
We give (1) an upper bound on the denominators of numerical boundary slopes and (2) an upper bound on the differences between two numerical boundary slopes, for Montesinos knot exteriors.
We obtain a series of lower bounds for the product set of combinatorial cubes, as well as some non--trivial upper estimates for the multiplicative energy of such sets.
We study density and partition properties of polynomial equations in prime variables. We consider equations of the form $a_1h(x_1) + \cdots + a_sh(x_s)=b$, where the $a_i$ and $b$ are fixed coefficients, and $h$ is an arbitrary integer…
We derive several new bounds for the problem of difference sets with local properties, such as establishing the super-linear threshold of the problem. For our proofs, we develop several new tools, including a variant of higher moment…
The Ramsey number is of vital importance in Ramsey's theorem. This paper proposed a novel methodology for constructing Ramsey graphs about R(3,10), which uses Artificial Bee Colony optimization(ABC) to raise the lower bound of Ramsey number…
Combinatorics on multisets is used to deduce new upper and lower bounds on the number of numerical semigroups of each given genus, significantly improving existing ones. In particular, it is proved that the number $n_g$ of numerical…
We improve the upper bound on the Ramsey number R(3,10) from 42 to 41. Hence R(3,10) is equal to 40 or 41.
We present an extension of the Delsarte linear programming method. For several dimensions it yields improved upper bounds for kissing numbers and for spherical codes. Musin's recent work on kissing numbers in dimensions three and four can…
In the context of compressed sensing (CS), this paper considers the problem of reconstructing sparse signals with the aid of other given correlated sources as multiple side information. To address this problem, we theoretically study a…
The $r$-color size-Ramsey number of a $k$-uniform hypergraph $H$, denoted by $\hat{R}_r(H)$, is the minimum number of edges in a $k$-uniform hypergraph $G$ such that for every $r$-coloring of the edges of $G$ there exists a monochromatic…
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.
This paper proposes lower bounds on a quantity called $L^p$-norm joint spectral radius, or in short, $p$-radius, of a finite set of matrices. Despite its wide range of applications to, for example, stability analysis of switched linear…
Let H_1, ..., H_k be graphs. The multicolor Ramsey number r(H_1,...,H_k) is the minimum integer r such that in every edge-coloring of K_r by k colors, there is a monochromatic copy of H_i in color i for some 1 <= i <= k. In this paper, we…
New bounds on the cardinality of permutation codes equipped with the Ulam distance are presented. First, an integer-programming upper bound is derived, which improves on the Singleton-type upper bound in the literature for some lengths.…
New lower bounds on the minimum average Hamming distance of binary codes are derived. The bounds are obtained using linear programming approach.
Another approach to constructing an upper bound for the Riemann-Farey sum is described.
Spark plays a great role in studying uniqueness of sparse solutions of the underdetermined linear equations. In this article, we derive a new lower bound of spark. As an application, we obtain a new criterion for the uniqueness of sparse…