Let G be an abelian group. For a subset A ⊂ G, denote by 2 ∧ A the set of sums of two
different elements of A. A conjecture by Erdős and Heilbronn, first proved by Dias da Silva and …

… define its restricted sumset Aˆ + A to be the set of sums of two … We say A is a restricted-sum-dominant
set if | Aˆ + A|>| A− A| . … restricted-sum-dominant sets. As a by-product, we improve …

… classes modulo p that can be written as the sum of two distinct elements of A. This had been
… On the other hand, by the very definition of C, f(a1,... ,an) = 0 for all a1 ∈ A1,... ,an ∈ An. So …

… Our proof of Theorem 1.6 depends heavily on a new identity similar … In this section, we pose
16 open conjectures on sums of … We also have the following conjecture on restricted sums of …

… sum … on sum formulas was realized by constructing refinements of (4) when considering
only even arguments sj = 2cj, cj ∈ N, j = 1,...,K, (we refer to this kind of sums as restricted sum …

… Let V{[0] be an m-dimensional vector space over the field F and let f be a linear operator
on V. We use Pf to denote the minimal polynomial of f and :f, 1 |}}}| :f, m=Pf to denote the …

… integer h, the sumset hA and the restricted sumset hˆA are fundamental objects in the … sum
of h elements of A, whereas the sumset hˆA is the set of integers that can be written as the sum …

… We first recall some results on symmetric functions contained in [6, 7] with some modification.
Let \(\operatorname{Sym}\) be the subring of consisting of the formal power series of …

… Cayley sum graphs; we refer to Section 3.2 for more discussions. We also refer to Remark 3.6
on … Lagrange [20] and Nicolas [23] found a set of 6 integers such that the sum of any two of …

… This sum is currently too difficult to estimate, in that the restrictions on divisors depend on …
divisor sum derived in Theorem 2.1 above by looking at the sums where the divisors are …