Related papers: Regressive versions of Hindman's Theorem

Renyi's "thinning" operation on a discrete random variable is a natural discrete analog of the scaling operation for continuous random variables. The properties of thinning are investigated in an information-theoretic context, especially in…

The van Lambalgen theorem is a surprising result in algorithmic information theory concerning the symmetry of relative randomness. It establishes that for any pair of infinite sequences $A$ and $B$, $B$ is Martin-L\"of random and $A$ is…

We establish a Rademacher type theorem involving Hamiltonians $H(x,p)$ under very weak conditions in both of Euclidean and Carnot-Carath\'eodory spaces. In particular,$H(x,p)$ is assumed to be only measurable in the variable $x$, and to be…

A preparation theorem for compositions of restricted log-exp-analytic functions and power functions of the form $$h: \mathbb{R} \to \mathbb{R}, x \mapsto \left\{\begin{array}{ll} x^r, & x > 0, \\ 0, & \textnormal{ else, }…

The inverse Henderson problem refers to the determination of the pair potential which specifies the interactions in an ensemble of classical particles in continuous space, given the density and the equilibrium pair correlation function of…

We prove a new characterization of the Ramsey property of categories in terms of a generalized form of K\H{o}nig's tree lemma. Afterwards, we discuss its applications to structural Ramsey theory. In particular, we provide a new proof of the…

We apply the Dual Ramsey Theorem of Graham and Rothschild to prove the Ramsey property for classes of finite Boolean algebras with distinguished ideals. This allows us to compute the universal minimal flow of the group of automorphisms of…

We examine a version of Ramsey's theorem based on Tao, Gaspar and Kohlenbach's "finitary" infinite pigeonhole principle.We will show that the "finitary" infinite Ramsey's theorem naturally gives rise to statements at the level of the…

Hindman's Theorem states that in any finite coloring of the integers, there is an infinite set all of whose finite sums belong to the same color. This is much stronger than the corresponding finite form, stating that in any finite coloring…

We explain that Hadamard's global inverse function theorem very simply follows from the Hopf--Rinow theorem in Riemannian geometry.

We study the reverse mathematics of infinitary extensions of the Hales-Jewett theorem, due to Carlson and Simpson. These theorems have multiple applications in Ramsey's theory, such as the existence of finite big Ramsey numbers for the…

Assume the mapping $$A:\left\{ \begin{array}{ll} x_{1}=x+\omega+y+f(x,y), y_{1}=y+g(x,y), \end{array} \right. (x, y)\in \mathbb{T}^{d}\times B(r_{0}) $$ is reversible with respect to $G: (x, y)\mapsto (-x, y),$ and $| f |…

An elementary renewal theorem and a Blackwell theorem provided by Jasiulis-Go{\l}dyn et al. (2020) in a setting of Kendall convolutions are proved under weaker hypothesis and extended to the Gamma class. Convergence rates of the limits…

Assuming that both a function and its Fourier transform are dominated by a Gaussian of large variance, it is shown that the Hermite coefficients of the function decay exponentially. A sharp estimate for the rate of exponential decay is…

We provide several constructions for problems in Ramsey theory. First, we prove a superexponential lower bound for the classical 4-uniform Ramsey number $r_4(5,n)$, and the same for the iterated $(k-4)$-fold logarithm of the $k$-uniform…

Canonical formalism of the rank-three tensor model has recently been proposed, in which "local" time is consistently incorporated by a set of first class constraints. By brute-force analysis, this paper shows that there exist only two forms…

We give an abstract approach to finite Ramsey theory and prove a general Ramsey-type theorem. We deduce from it a self-dual Ramsey theorem, which is a new result naturally generalizing both the classical Ramsey theorem and the dual Ramsey…

We develop a semiclassical theory of modified gravity with nontrivial spacetime torsion. In particular, we show that the semiclassical treatment can be axiomatized in the case of Einstein--Cartan theory with a nonminimally coupled, free…

We derive the discrete version of the classical Helmholtz condition. Precisely, we state a theorem characterizing second order finite differences equations admitting a Lagrangian formulation. Moreover, in the affirmative case, we provide…

The celebrated canonical Ramsey theorem of Erd\H{o}s and Rado implies that for $2\leq k\in \mathbb{N}$, any colouring of the edges of $K_n$ with $n$ sufficiently large gives a copy of $C_{2k}$ which has one of three canonical colour…