Let Γ be an abelian group and g ≥ h ≥ 2 be integers. A set A ⊂ Γ is a Ch[g]-set if given any set X ⊂ Γ with |X | = h, and any set {k1, . . . , kg } ⊂ Γ , at least one of the translates X + ki is not contained in A. For any g ≥ h ≥ 2, we prove that if A ⊂ {1, 2, . . . , n} is a Ch[g]-set in Z, then |A| ≤ (g − 1)1/hn1−1/h + O(n1/2−1/2h). We show that for any integer n ≥ 1, there is a C3[3]-set A ...

A Sidon space is a subspace of an extension field over base in which the product any two elements can be factored uniquely, up to constants. This paper proposes new public-key cryptosystem multivariate type based on spaces, and has potential remain secure even if quantum supremacy attained. system, whose security relies hardness well-known MinRank problem, shown resilient several straightforwar...

We study the frequency of hypercyclicity of hypercyclic, non–weakly mixing linear operators. In particular, we show that on the space `(N), any sublinear frequency can be realized by a non–weakly mixing operator. A weaker but similar result is obtained for c0(N) or `(N), 1 < p <∞. Part of our results is related to some Sidon-type lacunarity properties for sequences of natural numbers.

The Sidon constant for the index set of nonzero m-homogeneous polynomials P in n complex variables is the supremum of the ratio between the l norm of the coefficients of P and the H(D) norm of P . We present an estimate which gives the right order of magnitude for this constant, modulo a factor depending exponentially on m. We use this result to show that the Bohr radius for the polydisc D is b...