Related papers: Difference Ramsey Numbers and Issai Numbers

Numerous practical medical problems often involve data that possess a combination of both sparse and non-sparse structures. Traditional penalized regularizations techniques, primarily designed for promoting sparsity, are inadequate to…

In this paper, we discuss an improvement of an algorithm to search for primes $p$ and coset-partitions of Z/pZ* that yield Ramsey algebras over Z/pZ. We also prove an upper bound on the modulus p in terms of the number of cosets. We have,…

We study solutions to the Egyptian fractions equation with the prime factors of the denominators constrained to lie in a fixed set of primes. We evaluate the effectiveness of the greedy algorithm in establishing bounds on such solutions.…

For two graphs $G,H$, the \emph{Ramsey number} $r(G,H)$ is the minimum integer $n$ such that any red/blue edge-coloring of $K_n$ contains either a red copy of $G$ or a blue copy of $H$. For two graphs $G,H$, the \emph{Gallai-Ramsey number}…

For functions of independent random variables, various upper and lower variance bounds are revisited in diverse settings. These are then specialized to the Bernoulli, Gaussian, infinitely divisible cases and to Banach space valued random…

Ramsey theory is a central and active branch of combinatorics. Although Ramsey numbers for graphs have been extensively investigated since Ramsey's work in the 1930s, there is still an exponential gap between the best known lower and upper…

We propose a new method for proving lower bounds on quantum query algorithms. Instead of a classical adversary that runs the algorithm with one input and then modifies the input, we use a quantum adversary that runs the algorithm with a…

It is observed that the conjugacy growth series of the infinite finitary symmetric group with respect to the generating set of transpositions is the generating series of the partition function. Other conjugacy growth series are computed,…

We study a probabilistic numerical method for the solution of both boundary and initial value problems that returns a joint Gaussian process posterior over the solution. Such methods have concrete value in the statistics on Riemannian…

This first extracted report contains all lower and upper bounds for e-numbers $e(3,k;n)$, for $n \leq 43$, that I know. All but 24 of them are known (exactly).Very little of the proofs is given. A few consequences for upper classical Ramsey…

There is increasing interest within the research community in the design and use of recursive probability models. Although there still remains concern about computational complexity costs and the fact that computing exact solutions can be…

We use the repeated averages hierarchy to prove a Ramsey theorem regarding uniform upper estimates of convex block sequences of weakly null sequences. The base case of the theorem recovers a result of Freeman.

An increasing sequence $(x_i)_{i=1}^n$ of positive integers is an $n$-term Egyptian underapproximation of $\theta \in (0,1]$ if $\sum_{i=1}^n \frac{1}{x_i} < \theta$. A greedy algorithm constructs an $n$-term underapproximation of $\theta$.…

Several physics-based algorithms for factorizing large number were recently published. A notable recent one by Schleich et al. uses Gauss sums for distinguishing between factors and non-factors. We demonstrate two NMR techniques that…

Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind of rooted forest with $k$ roots and that with $k+1$ roots on…

The Hales--Jewett theorem is one of the pillars of Ramsey theory, from which many other results follow. A celebrated theorem of Shelah says that Hales--Jewett numbers are primitive recursive. A key tool used in his proof, now known as the…

In this paper, we study three applications of recursion to problems in coding and random permutations. First, we consider locally recoverable codes with partial locality and use recursion to estimate the minimum distance of such codes. Next…

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…

This paper investigates two issues on identification of switched linear systems: persistence of excitation and numerical algorithms. The main contribution is a much weaker condition on the regressor to be persistently exciting that…

The Ramsey number $r_k(p, q)$ is the smallest integer $N$ that satisfies for every red-blue coloring on $k$-subsets of $[N]$, there exist $p$ integers such that any $k$-subset of them is red, or $q$ integers such that any $k$-subset of them…