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pro vyhledávání: '"Landman, Bruce"'
Autor:
Landman, Bruce, Robertson, Aaron
Publikováno v:
In Advances in Applied Mathematics May 2023 146
Let a and b be positive integers with a \leq b. An (a,b)-triple is a set {x,ax+d,bx+ 2d}, where x,d \geq 1. Define T(a,b;r) to be the least positive integer n such that any r-coloring of {1,2...,n} contains a monochromatic (a,b)-triple. Earlier resul
Externí odkaz:
http://arxiv.org/abs/1201.3842
For positive integers $s$ and $k_1, k_2, ..., k_s$, let $w(k_1,k_2,...,k_s)$ be the minimum integer $n$ such that any $s$-coloring $\{1,2,...,n\} \to \{1,2,...,s\}$ admits a $k_i$-term arithmetic progression of color $i$ for some $i$, $1 \leq i \leq
Externí odkaz:
http://arxiv.org/abs/0706.4420
Let $1 \leq a \leq b$ be integers. A triple of the form $(x,ax+d,bx+2d)$, where $x,d$ are positive integers is called an {\em (a,b)-triple}. The {\em degree of regularity} of the family of all $(a,b)$-triples, denoted dor($a,b)$, is the maximum integ
Externí odkaz:
http://arxiv.org/abs/math/0507588
For positive integers $r,k_0,k_1,...,k_{r-1},$ the van der Waerden number $w(k_0,k_1,...,k_{r-1})$ is the least positive integer $n$ such that whenever $\{1,2,...,n\}$ is partitioned into $r$ sets $S_{0},S_{1},...,S_{r-1}$, there is some $i$ so that
Externí odkaz:
http://arxiv.org/abs/math/0507019
Autor:
Landman, Bruce M., Robertson, Aaron
For $S$ a set of positive integers, and $k$ and $r$ fixed positive integers, denote by $f(S,k;r)$ the least positive integer $n$ (if it exists) such that within every $r$-coloring of $\{1,2,...,n\}$ there must be a monochromatic sequence $\{x_{1},x_{
Externí odkaz:
http://arxiv.org/abs/math/0302041
Autor:
Landman, Bruce, Robertson, Aaron
Van der Waerden's classical theorem on arithmetic progressions states that for any positive integers k and r, there exists a least positive integer, w(k,r), such that any r-coloring of {1,2,...,w(k,r)} must contain a monochromatic k-term arithmetic p
Externí odkaz:
http://arxiv.org/abs/math/9910092
Publikováno v:
In Advances in Applied Mathematics 2006 37(1):124-128