A set of nonnegative integers is called a Sidon if there no 4-tuple, i.e., (a, b, c, d) in with + b = c d and {a, b} ∩ {c, d} ∅. Cameron Erdős proposed the problem determining number sets [n]. Results Kohayakawa, Lee, Rodl Samotij, Saxton Thomason have established that between 2 (1.16+o(1))√n (6.442+o(1))√n . An α-generalized [n] at most α 4-tuples. One way to extend estimate We show (n/ log4 n...

Let C(T ) be a generalized Coxeter group, which has a natural map onto one of the classical Coxeter groups, either Bn or Dn. Let CY (T ) be a natural quotient of C(T ), and if C(T ) is simply-laced (which means all the relations between the generators has order 2 or 3), CY (T ) is a generalized Coxeter group, too . Let At,n be a group which contains t Abelian groups generated by n elements. The...

In this paper, we provide two types of boundary path groupoids from a generalized Boolean dynamical system (B,L,θ,Iα). For the first groupoid, associate an inverse semigroup to and use tight spectrum T as unit space groupoid Γ(B,L,θ,Iα) that is isomorphic Gtight. The other one defined Renault-Deaconu Γ(∂E,σE) arising topological correspondence E associated with system. We then prove homeomorphi...