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
In this dissertation, we present new methods in the computation of Rado numbers. These methods are a...
For every positive integer $a$, let $n = R_{ZS}(a)$ be the least integer, provided it exists, such t...
AbstractFor integers c⩾0 and k⩾1, let R=R(c,k) be the least integer, provided it exists, such that e...
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 ...
AbstractFor integers c⩾0 and k⩾1, let R=R(c,k) be the least integer, provided it exists, such that e...
AbstractFor all integers m,n, such that 3⩽m⩽n, let r(S(m),S(n)) represent the least integer such tha...
AbstractFor all integers m⩾3 and all natural numbers a1,a2,…,am−1, let n=R(a1,a2,…,am−1) represent t...
AbstractFor positive integers a1,a2,…,am, we determine the least positive integer R(a1,…,am) such th...
AbstractFor integers n⩾1 and k⩾0, let Mk(n) represent the minimum number of monochromatic solutions ...
AbstractThe 2-color Rado number for the equation x1+x2−2x3=c, which for each constant c∈Z we denote ...
AbstractIf L1 and L2 are linear equations, then the disjunctive Rado number of the set {L1,L2} is th...
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...
In this dissertation, we present new methods in the computation of Rado numbers. These methods are a...
For every positive integer $a$, let $n = R_{ZS}(a)$ be the least integer, provided it exists, such t...
AbstractFor integers c⩾0 and k⩾1, let R=R(c,k) be the least integer, provided it exists, such that e...
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 ...
AbstractFor integers c⩾0 and k⩾1, let R=R(c,k) be the least integer, provided it exists, such that e...
AbstractFor all integers m,n, such that 3⩽m⩽n, let r(S(m),S(n)) represent the least integer such tha...
AbstractFor all integers m⩾3 and all natural numbers a1,a2,…,am−1, let n=R(a1,a2,…,am−1) represent t...
AbstractFor positive integers a1,a2,…,am, we determine the least positive integer R(a1,…,am) such th...
AbstractFor integers n⩾1 and k⩾0, let Mk(n) represent the minimum number of monochromatic solutions ...
AbstractThe 2-color Rado number for the equation x1+x2−2x3=c, which for each constant c∈Z we denote ...
AbstractIf L1 and L2 are linear equations, then the disjunctive Rado number of the set {L1,L2} is th...
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...
In this dissertation, we present new methods in the computation of Rado numbers. These methods are a...
For every positive integer $a$, let $n = R_{ZS}(a)$ be the least integer, provided it exists, such t...
AbstractFor integers c⩾0 and k⩾1, let R=R(c,k) be the least integer, provided it exists, such that e...
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