A generalization of Kneser's Addition Theorem

  title={A generalization of Kneser's Addition Theorem},
  author={Matt DeVos and Luis A. Goddyn and Bojan Mohar},
  journal={Advances in Mathematics},

On n-Sums in an Abelian Group

It is proved that either ng ∈ Σ n (S) for every term g in S whose multiplicity is at least ${\mathsf h}$ (S), ⩾ min{n + 1, |S| − n + | supp (S)| − 1}, where |supp(S)| denotes the number of distinct terms that occur in S.

Character and Linear Algebraic Methods: Snevily’s Conjecture

In this chapter, we present another (and very recent) application of the method of Character Sums. Let G be a finite abelian group and let A, B⊆G be subsets of equal cardinality (say) k. Then we

Weighted subsequence sums in finite Abelian Groups

A well-known result of Erdős-Ginzburg-Ziv [32] says that, given a sequence S of 2n− 1 integers, there is a subsequence S ′ of S with length n such that the sum of the terms of S ′ is zero modulo n.

A weighted generalization of two theorems of Gao

AbstractLet G be a finite abelian group and let A⊆ℤ be nonempty. Let DA(G) denote the minimal integer such that any sequence over G of length DA(G) must contain a nontrivial subsequence s1⋯sr such

Number of Weighted Subsequence Sums with Weights in {1, –1}

A lower bound on the number of A-weighted n-sums of the sequence S is obtained on the existence of zero-smooth subsequences and the DeVos–Goddyn–Mohar Theorem is obtained.

Matchings in matroids over abelian groups

We formulate and prove matroid analogues of results concerning matchings in groups. A matching in an abelian group (G,+) is a bijection f : A → B between two finite subsets A,B of G satisfying a +

Two conjectures on an addition theorem

Theorem 1.1 (EGZ Theorem). Let G denote a cyclic group of order n and S ∈ F(G) be a sequence of length 2n− 1 over G. Then 0 ∈ ∑ n(S). The length 2n− 1 is sharp in view of the example S = 0n−1gn−1,

On a conjecture of Zhuang and Gao

Let G be a multiplicatively written finite group. We denote by E(G) the smallest integer t such that every sequence of t elements in G contains a product-one subsequence of length |G|. In 1961,



Theorem in the Additive Number Theory

THEOREM. Each set of 2n-1 integers contains some subset of n elements the sum of which is a multiple of n. PROOF. Assume first n = p (p prime). Our theorem is trivial for p = 2, thus henceforth p >

On a Conjecture of Hamidoune for Subsequence Sums

Let G be an abelian group of order m, let S be a sequence of terms from G with k distinct terms, let m ∧ S denote the set of all elements that are a sum of some m-term subsequence of S, and let |S|

A Combinatorial Problem on Finite Abelian Groups

Abstract In this paper the following theorem is proved. Let G be a finite Abelian group of order n . Then, n + D ( G )−1 is the least integer m with the property that for any sequence of m elements a

On weighted sums in abelian groups

On a combinatorial problem of Erdős

Let C(n, m) denote the binomial coefficient n!/(m!n-m!). Let S be a set containing N elements and let X be a collection of subsets of S with the property that if A, B and C are distinct elements of

The Number of k-Sums Modulo k

Abstract Let a1, …, ar be a sequence of elements of Z k, the integers modulo k. Calling the sum of k terms of the sequence a k-sum, how small can the set of k-sums be? Our aim in this paper is to

On a Combinatorial Theorem of Erdös, Ginzburg and Ziv

It is proved that the sums of the n-subsequences of μ must include a non-null subgroup and this last result reduces to the Erdos–Ginzburg–Ziv theorem for k=2.

On A Combinatorial Problem of Erdös

A family of sets is said to possess property if there exists a set such that and for every We consider the following question raised by P. Erdös |1|: let n and N be positive integers, n ≥ 2 and N ≥