AbstractFor all integers m⩾3 and all natural numbers a1,a2,…,am−1, let n=R(a1,a2,…,am−1) represent the least integer such that for every 2-coloring of the set {1,2,…,n} there exists a monochromatic solution to a1x1+a2x2+⋯+am−1xm−1=xm. Let t=min{a1,a2,…,am−1} and b=a1+a2+⋯+am−1−t. In this paper it is shown that whenever t=2, R(a1,a2,…,am−1)=2b2+9b+8. It is also shown that for all values of t, R(a1,a2,…,am−1)⩾tb2+(2t2+1)b+t3
AbstractFor integers n⩾1 and k⩾0, let Mk(n) represent the minimum number of monochromatic solutions ...
AbstractWe prove that Rado's Boundedness Conjecture from Richard Rado's 1933 famous dissertation Stu...
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...
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...
AbstractIf it exists, the smallest number N = Rk(∑) is called the kth Rado number of a given system ...
AbstractThe 2-color Rado number for the equation x1+x2−2x3=c, which for each constant c∈Z we denote ...
AbstractFor integers c⩾0 and k⩾1, let R=R(c,k) be the least integer, provided it exists, such that e...
AbstractIn the case of existence the smallest numberN=Rakis called a Rado number if it is guaranteed...
AbstractIf L1 and L2 are linear equations, then the disjunctive Rado number of the set {L1,L2} is th...
AbstractFor positive integers a1,a2,…,am, we determine the least positive integer R(a1,…,am) such th...
Given a linear equation $\mathcal{E}$, the $k$-color Rado number $R_k(\mathcal{E})$ is the smallest ...
A set is called Totally Multicolored (TMC) if no elements in the set are colored the same. For all n...
For every positive integer $a$, let $n = R_{ZS}(a)$ be the least integer, provided it exists, such t...
AbstractFor integers n⩾1 and k⩾0, let Mk(n) represent the minimum number of monochromatic solutions ...
AbstractWe prove that Rado's Boundedness Conjecture from Richard Rado's 1933 famous dissertation Stu...
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...
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...
AbstractIf it exists, the smallest number N = Rk(∑) is called the kth Rado number of a given system ...
AbstractThe 2-color Rado number for the equation x1+x2−2x3=c, which for each constant c∈Z we denote ...
AbstractFor integers c⩾0 and k⩾1, let R=R(c,k) be the least integer, provided it exists, such that e...
AbstractIn the case of existence the smallest numberN=Rakis called a Rado number if it is guaranteed...
AbstractIf L1 and L2 are linear equations, then the disjunctive Rado number of the set {L1,L2} is th...
AbstractFor positive integers a1,a2,…,am, we determine the least positive integer R(a1,…,am) such th...
Given a linear equation $\mathcal{E}$, the $k$-color Rado number $R_k(\mathcal{E})$ is the smallest ...
A set is called Totally Multicolored (TMC) if no elements in the set are colored the same. For all n...
For every positive integer $a$, let $n = R_{ZS}(a)$ be the least integer, provided it exists, such t...
AbstractFor integers n⩾1 and k⩾0, let Mk(n) represent the minimum number of monochromatic solutions ...
AbstractWe prove that Rado's Boundedness Conjecture from Richard Rado's 1933 famous dissertation Stu...
In this dissertation, we present new methods in the computation of Rado numbers. These methods are a...
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