Let A and B be two affinely generating sets of ℤ2n. As usual, we denote their Minkowski sum
by A+ B. How small can A+ B be, given the cardinalities of A and B? We give a tight answer …

Let G be a group. We study the minimal sumset (or product set) size μG (r, s)= min {| A⋅ B|},
where A, B range over all subsets of G with cardinality r, s respectively. The function μG has …

Let G be a group written multiplicatively. We say that G has the small sumsets property if for
all positive integers r, s≤| G|, there exist subsets A, B⊂ G such that| A|= r,| B|= s and| A⋅ …

For any group G and any set A, a cellular automaton (CA) is a transformation of the
configuration space A^ G defined via a finite memory set and a local function. Let CA (G; A) …

The Cauchy-Davenport theorem states that, if p is prime and A, B are nonempty subsets of
cardinality r, s in Z/pZ, the cardinality of the sumset A+ B={a+ b| a∈ A, b∈ B} is bounded …

Let G be an arbitrary group. For any subsets A and B of G, let A* B={a* b; a∈ A, b∈ B}
where*'is the binary operation on G. By μ G (r, s), we denote the minimum cardinality of the …

Given a group G and positive integers r, s≤| G|, we denote by μG (r, s) the least possible
size of a product set AB={ab∣ a∈ A, b∈ B}, where A, B run over all subsets of G of size r, s …

For integers $ m $ and $ n $, the Baumslag-Solitar groups, denoted as $ BS (m, n) $, are
groups generated by two elements with a single defining relation: $ BS (m, n)=\langle a, b …

arXiv:2411.02365v1 [math.NT] 4 Nov 2024 Page 1 arXiv:2411.02365v1 [math.NT] 4 Nov 2024
PROBLEMS IN ADDITIVE NUMBER THEORY, VI: SIZES OF SUMSETS MELVYN B …

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