AbstractIn the case of existence the smallest numberN=Rakis called a Rado number if it is guaranteed that anyk-coloring of the numbers 1,2,…,Ncontains a monochromatic solution of a given system of linear equations. We will determine Rak(a,b) for the equationa(x+y)=bzifb=2 andb=a+1. Also, the case of monochromatic sequences {xn} generated bya(xn+xn+1)=bxn+2 is discussed
The 2-color Rado number for the equation x1+x 2-2x3=c, which for each constant c∈Z we denote by S1(c...
An equation L is said to have a finite 4-color Rado number if there exists a least integer n, such t...
AbstractWe prove that Rado's Boundedness Conjecture from Richard Rado's 1933 famous dissertation Stu...
AbstractIf it exists, the smallest number N = Rk(∑) is called the kth Rado number of a given system ...
AbstractIn the case of existence the smallest numberN=Rakis called a Rado number if it is guaranteed...
AbstractIf it exists, the smallest number N = Rk(∑) is called the kth Rado number of a given system ...
For relatively prime positive integers a and b, let n = R(a,b) denote the least positive integer suc...
AbstractFor all integers m⩾3 and all natural numbers a1,a2,…,am−1, let n=R(a1,a2,…,am−1) represent t...
AbstractThere exists a minimum integer N such that any 2-coloring of {1,2,…,N} admits a monochromati...
AbstractFor integers c⩾0 and k⩾1, let R=R(c,k) be the least integer, provided it exists, such that e...
In this dissertation, we present new methods in the computation of Rado numbers. These methods are a...
AbstractFor positive integers a1,a2,…,am, we determine the least positive integer R(a1,…,am) such th...
AbstractIf L1 and L2 are linear equations, then the disjunctive Rado number of the set {L1,L2} is th...
Given a linear equation, the least integer n, provided it exists, such that for every t-coloring of ...
AbstractThe 2-color Rado number for the equation x1+x2−2x3=c, which for each constant c∈Z we denote ...
The 2-color Rado number for the equation x1+x 2-2x3=c, which for each constant c∈Z we denote by S1(c...
An equation L is said to have a finite 4-color Rado number if there exists a least integer n, such t...
AbstractWe prove that Rado's Boundedness Conjecture from Richard Rado's 1933 famous dissertation Stu...
AbstractIf it exists, the smallest number N = Rk(∑) is called the kth Rado number of a given system ...
AbstractIn the case of existence the smallest numberN=Rakis called a Rado number if it is guaranteed...
AbstractIf it exists, the smallest number N = Rk(∑) is called the kth Rado number of a given system ...
For relatively prime positive integers a and b, let n = R(a,b) denote the least positive integer suc...
AbstractFor all integers m⩾3 and all natural numbers a1,a2,…,am−1, let n=R(a1,a2,…,am−1) represent t...
AbstractThere exists a minimum integer N such that any 2-coloring of {1,2,…,N} admits a monochromati...
AbstractFor integers c⩾0 and k⩾1, let R=R(c,k) be the least integer, provided it exists, such that e...
In this dissertation, we present new methods in the computation of Rado numbers. These methods are a...
AbstractFor positive integers a1,a2,…,am, we determine the least positive integer R(a1,…,am) such th...
AbstractIf L1 and L2 are linear equations, then the disjunctive Rado number of the set {L1,L2} is th...
Given a linear equation, the least integer n, provided it exists, such that for every t-coloring of ...
AbstractThe 2-color Rado number for the equation x1+x2−2x3=c, which for each constant c∈Z we denote ...
The 2-color Rado number for the equation x1+x 2-2x3=c, which for each constant c∈Z we denote by S1(c...
An equation L is said to have a finite 4-color Rado number if there exists a least integer n, such t...
AbstractWe prove that Rado's Boundedness Conjecture from Richard Rado's 1933 famous dissertation Stu...
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