Results 11 to 20 of about 6,008,885 (289)
Lines in Euclidean Ramsey Theory [PDF]
Discrete & Computational Geometry, 2018 Let $\ell_m$ be a sequence of $m$ points on a line with consecutive points of distance one. For every natural number $n$, we prove the existence of a red/blue-coloring of $\mathbb{E}^n$ containing no red copy of $\ell_2$ and no blue copy of $\ell_m$ for any $m \geq 2^{cn}$. This is best possible up to the constant $c$ in the exponent. It also answers a
Conlon, D, Fox, J
semanticscholar +11 more sources
Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory [PDF]
Lecture notes in mathematics, 2019 The goal of this present manuscript is to introduce the reader to the nonstandard method and to provide an overview of its most prominent applications in Ramsey theory and combinatorial number theory.
Mauro Di Nasso +2 more
semanticscholar +5 more sources
Using Ramsey Theory to Measure Unavoidable Spurious Correlations in Big Data
Axioms, 2019 Given a dataset, we quantify the size of patterns that must always exist in the dataset. This is done formally through the lens of Ramsey theory of graphs, and a quantitative bound known as Goodman’s theorem.
Micheal Pawliuk +1 more
doaj +3 more sources
Ramsey Theory in Noncommutative Semigroups [PDF]
Transactions of the American Mathematical Society, 1992 By utilizing ultrafilters we give a general version of the Central Sets Theorem [ 6 6 , Proposition 8.21]. This enables us to derive noncommutative versions of van der Waerden’s Theorem and several of its generalizations. We also derive some standard results, including the Hales-Jewett Theorem.
Vitaly Bergelson, Neil Hindman
openalex +2 more sources
Ramsey theory for hypergroups [PDF]
Semigroup Forum, 2019 In this paper, Ramsey theory for discrete hypergroups is introduced with emphasis on polynomial hypergroups, discrete orbit hypergroups and hypergroup deformations of semigroups. In this context, new notions of Ramsey principle for hypergroups and $ $-Ramsey hypergroup, $0 \leq <1,$ are defined and studied.
Kenneth A. Ross +2 more
openaire +5 more sources
The Electronic Journal of Combinatorics, 2004 There are many interesting applications of Ramsey theory, these include results in number theory, algebra, geometry, topology, set theory, logic, ergodic theory, information theory and theoretical computer science. Relations of Ramsey-type theorems to various fields in mathematics are well documented in published books and monographs.
Vera Rosta
openalex +3 more sources
MONOID ACTIONS AND ULTRAFILTER METHODS IN RAMSEY THEORY [PDF]
Forum of Mathematics, Sigma, 2019 First, we prove a theorem on dynamics of actions of monoids by endomorphisms of semigroups. Second, we introduce algebraic structures suitable for formalizing infinitary Ramsey statements and prove a theorem that such statements are implied by the ...
SŁAWOMIR SOLECKI
doaj +2 more sources
Recent developments in graph Ramsey theory [PDF]
Surveys in Combinatorics, 2015 Given a graph $H$, the Ramsey number $r(H)$ is the smallest natural number $N$ such that any two-colouring of the edges of $K_N$ contains a monochromatic copy of $H$.
David Conlon, Jacob Fox, Benny Sudakov
openalex +3 more sources
Exponential patterns in arithmetic Ramsey theory [PDF]
, 2017 We show that for every finite colouring of the natural numbers there exists $a,b >1$ such that the triple $\{a,b,a^b\}$ is monochromatic. We go on to show the partition regularity of a much richer class of patterns involving exponentiation.
Julian Sahasrabudhe
openalex +3 more sources
Collectively enhanced Ramsey readout by cavity sub- to superradiant transition [PDF]
Nature CommunicationsWhen an inverted ensemble of atoms is tightly packed on the scale of its emission wavelength or when the atoms are collectively strongly coupled to a single cavity mode, their dipoles will align and decay rapidly via a superradiant burst.
Eliot A. Bohr +8 more
doaj +2 more sources