Partition Regular Inequalities
نویسندگان
چکیده
منابع مشابه
Partition Regular Systems of Linear Inequalities
3 (m,p,c)-sets 59 4 Canonical Results 63 5 Coloring Objects of Higher Rank 65 1 Introduction In 1930 Ramsey published his paper On a problem in formal logic 12]. He established a result, nowadays known as Ramsey's Theorem: Let k and r be positive integers. Then for every r-coloring of the k-element subsets of ! there exists an innnite subset S ! such that all k-element subsets of S are colored ...
متن کاملMultiply partition regular matrices
Let A be a finite matrix with rational entries. We say that A is doubly image partition regular if whenever the set N of positive integers is finitely coloured, there exists ~x such that the entries of A~x are all the same colour (or monochromatic) and also, the entries of ~x are monochromatic. Which matrices are doubly image partition regular? More generally, we say that a pair of matrices (A,...
متن کاملConsistency for partition regular equations
It is easy to deduce from Ramsey’s Theorem that, given positive integers a1, a2, . . . , am and a finite colouring of the set N of positive integers, there exists an injective sequence (xi) ∞ i=1 with all sums of the form ∑m i=1 aixri (r1 < r2 < · · · < rm) lying in the same colour class. The consistency version of this result, namely that, given positive integers a1, a2, . . . , am and b1, b2,...
متن کاملIndependence for partition regular equations
A matrix A is said to be partition regular (PR) over a subset S of the positive integers if whenever S is finitely coloured, there exists a vector x, with all elements in the same colour class in S, which satisfies Ax = 0. We also say that S is PR for A. Many of the classical theorems of Ramsey Theory, such as van der Waerden’s Theorem and Schur’s Theorem, may naturally be interpreted as statem...
متن کاملRefinements of Some Partition Inequalities
In the present paper we initiate the study of a certain kind of partition inequality, by showing, for example, that if M 5 is an integer and the integers a and b are relatively prime to M and satisfy 1 a < b < M/2, and the c(m,n) are defined by 1 (sqa, sqM a; qM )1 1 (sqb, sqM b; qM )1 := X
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1998
ISSN: 0195-6698
DOI: 10.1006/eujc.1998.0213