Given a (multi) set S of n positive integers and a target integer u, the subset sum problem is
to decide if there is a subset of S that sums up to u. We present a series of new algorithms …

Given n positive integers, the Modular Subset Sum problem asks if a subset adds up to a
given target t modulo a given integer m. This is a natural generalization of the Subset Sum …

Abstract We revisit the Subset Sum problem over the finite cyclic group ℤ m for some given
integer m. A series of recent works has provided near-optimal algorithms for this problem …

Using the polynomial method in additive number theory, this article establishes a new
addition theorem for the set of subsums of a set satisfying A∩(− A)=∅ in ℤ/p ℤ …

The well-known middle levels conjecture asserts that for every integer n≧1, all binary
strings of length 2 (n+ 1) with exactly n+ 1 many 0s and 1s can be ordered cyclically so that …

Let G be an additive, finite abelian group. The critical number cr (G) of G is the smallest
positive integer ℓ such that for every subset S⊂ G∖{0} with| S|⩾ ℓ the following holds: Every …

Let A be a sequence of rk terms which is made up of k distinct integers each appearing
exactly r times in A. The sum of all terms of a subsequence of A is called a subsequence …

Denoting by Σ (S) the set of subset sums of a subset S of a finite abelian group G, we prove
that| Σ (S)|⩾| S|(| S|+ 2) 4− 1 whenever S is symmetric,| G| is odd and Σ (S) is aperiodic. Up to …

Let $ A $ be a set of positive integers. We define a positive integer $ n $ as an $ A $-practical
number if every positive integer from the set $\left\{1,\ldots,\sum_ {d\in A, d\mid n} d\right\} …

Let $ G $ be a multiplicatively written finite group. The critical number $\mathsf {cr}(G) $ of $
G $ is the smallest integer $ t $ such that for every subset $ S $ of $ G\setminus\{1\} $ with …