# A generalization of Kneser's Addition Theorem

```@article{DeVos2009AGO,
title={A generalization of Kneser's Addition Theorem},
author={Matt DeVos and Luis A. Goddyn and Bojan Mohar},
year={2009},
volume={220},
pages={1531-1548}
}```
• Published 20 March 2009
• Mathematics

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## References

SHOWING 1-10 OF 40 REFERENCES

### 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 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

• Mathematics
• 1999
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

• Mathematics
Combinatorics, Probability and Computing
• 1998
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.

• Mathematics