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CONTINUOUS COLORINGS ASSOCIATED WITH CERTAIN CHARACTERISTICS OF THE CONTINUUM
CONTINUOUS COLORINGS ASSOCIATED CERTAIN CHARACTERISTICS
2015/8/17
A coloring c:[X]n → Z is said to be irreducible if for every Y; X of equal cardinality c00[Y ]n = Z. The focus of this note will be to show that there are continuous irreducible colorings on sets of r...
Open colorings,the continuum and the second uncountable cardinal
Open colorings the continuum second uncountable cardinal
2015/8/17
The purpose of this article is to analyze the cardinality of the continuum using Ramsey theoretic statements about open colorings or “open coloring axioms.” In particular I will show that the conjunct...
The purpose of this article is to prove the relative consistency of certain statements about open colorings with 2ℵ0 < 2ℵ1. In particular both OCA and the statement that every 1-1 function...
Monochromatic 4-term arithmetic progressions in 2-colorings of $\mathbb Z_n$
Monochromatic 4-term arithmetic progressions Combinatorics Number Theory
2011/9/8
Abstract: This paper is motivated by a recent result of Wolf \cite{wolf} on the minimum number of monochromatic 4-term arithmetic progressions(4-APs, for short) in $\Z_p$, where $p$ is a prime number....
Three-Colorings of Cubic Graphs and Tensor Operators
3-colorings of cubic planar graphs tensor algebras
2010/12/6
Penrose’s work [6] established a connection between the edge 3-colorings of cubic planar graphs and tensor algebras. We exploit this point of view in order to get algebraic representations of the cate...
On minimal colorings without monochromatic solutions to a linear equation
minimal colorings without monochromatic solutions linear equation
2010/12/9
For a ring R and system L of linear homogeneous equations, we call a coloring of the nonzero
elements of R minimal for L if there are no monochromatic solutions to L and the coloring uses as few colo...
A 2-coloring of the n-cube in the n-dimensional Euclidean space can be considered as an assignment of weights of 1 or 0 to the vertices. Such a colored n-cube is said to be balanced if its center of m...