AbstractFor positive integers a1,a2,…,am, we determine the least positive integer R(a1,…,am) such that for every 2-coloring of the set [1,n]={1,…,n} with n⩾R(a1,…,am) there exists a monochromatic solution to the equation a1x1+⋯+amxm=x0 with x0,…,xm∈[1,n]. The precise value of R(a1,…,am) is shown to be av2+v−a, where a=min{a1,…,am} and v=∑i=1mai. This confirms a conjecture of B. Hopkins and D. Schaal
In this dissertation, we present new methods in the computation of Rado numbers. These methods are a...
AbstractFor all integers m⩾3 and all natural numbers a1,a2,…,am−1, let n=R(a1,a2,…,am−1) represent t...
AbstractThe 2-color Rado number for the equation x1+x2−2x3=c, which for each constant c∈Z we denote ...
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...
For relatively prime positive integers a and b, let n = R(a,b) denote the least positive integer suc...
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...
The 2-color Rado number for the equation x1+x 2-2x3=c, which for each constant c∈Z we denote by S1(c...
AbstractIf L1 and L2 are linear equations, then the disjunctive Rado number of the set {L1,L2} is th...
AbstractThere exists a minimum integer N such that any 2-coloring of {1,2,…,N} admits a monochromati...
AbstractIf it exists, the smallest number N = Rk(∑) is called the kth Rado number of a given system ...
Given a linear equation, the least integer n, provided it exists, such that for every t-coloring of ...
AbstractIn the case of existence the smallest numberN=Rakis called a Rado number if it is guaranteed...
An equation L is said to have a finite 4-color Rado number if there exists a least integer n, such t...
In this dissertation, we present new methods in the computation of Rado numbers. These methods are a...
AbstractFor all integers m⩾3 and all natural numbers a1,a2,…,am−1, let n=R(a1,a2,…,am−1) represent t...
AbstractThe 2-color Rado number for the equation x1+x2−2x3=c, which for each constant c∈Z we denote ...
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...
For relatively prime positive integers a and b, let n = R(a,b) denote the least positive integer suc...
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...
The 2-color Rado number for the equation x1+x 2-2x3=c, which for each constant c∈Z we denote by S1(c...
AbstractIf L1 and L2 are linear equations, then the disjunctive Rado number of the set {L1,L2} is th...
AbstractThere exists a minimum integer N such that any 2-coloring of {1,2,…,N} admits a monochromati...
AbstractIf it exists, the smallest number N = Rk(∑) is called the kth Rado number of a given system ...
Given a linear equation, the least integer n, provided it exists, such that for every t-coloring of ...
AbstractIn the case of existence the smallest numberN=Rakis called a Rado number if it is guaranteed...
An equation L is said to have a finite 4-color Rado number if there exists a least integer n, such t...
In this dissertation, we present new methods in the computation of Rado numbers. These methods are a...
AbstractFor all integers m⩾3 and all natural numbers a1,a2,…,am−1, let n=R(a1,a2,…,am−1) represent t...
AbstractThe 2-color Rado number for the equation x1+x2−2x3=c, which for each constant c∈Z we denote ...
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