All Questions
Tagged with abelian-groups additive-combinatorics
8 questions
3
votes
1
answer
169
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Maximal zero-sum free sequences of $C_3^n$
I am working on the Davenport constant for groups, $D(G)$, which is the minimal number $d$ such that every sequence or multiset of $d$ elements of the group $G$ always contains some non-empty zero-sum ...
7
votes
0
answers
116
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A conjecture on circular permutations of n elements in an abelian group of odd order
In 2013 I formulated the following conjecture in additive combinatorics.
Conjecture. Let $G$ be an additive abelian group of odd order, and let $A$ be a subset of $G$ with $|A|=n>2$. Then, there is ...
- 15.6k
6
votes
0
answers
147
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When is $\{s_2-s_1,s_3-s_2,s_1-s_3\}\cap S$ non-empty for any $s_1,s_2,s_3\in S$?
A subset $S$ of an abelian group is a subgroup if and only if it is closed under taking differences; that is, the difference of any two elements of $S$ is in $S$. Suppose, however, that we only know ...
- 23k
3
votes
1
answer
153
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On decomposition of finite Abelian groups
It is easy to see that for any finite Abelian group $G$ and any numbers $a,b$ with $|G|=ab$ there exist a subgroup $A\subset G$ and a subset $B\subset G$ such that $|A|=a$, $|B|=b$ and $G=A+B$, where $...
- 42k
6
votes
1
answer
332
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Zero-sum sets in union-closed families
The Davenport constant $D(G)$ of a finite abelian group $G$ is the minimum integer $n$ such that whenever $a_1, \ldots, a_n \in G$ (not necessarily distinct), there is a non-empty $I \subseteq [n]$ ...
- 1,169
9
votes
0
answers
298
views
An abstract zero-sum problem
I would like to know whether the problem described below has appeared in the literature and/or whether similar questions have been studied. I would be very happy to find some references or, if none ...
- 1,169
5
votes
2
answers
387
views
Size of distinct sums in A
Let $G$ be an abelian group. Let $A\subset G$ be a finite set. $\sum_A$ is defined as: $$\left\{\sum_{b\in B}b \mid B\subset A\right\}$$ Is there any result similar to Freiman's Theorem for $\sum_A$? ...
- 901
16
votes
4
answers
1k
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Zero-sum partition of an abelian group
This is a question I have been asking myself some 5 years ago. I later got bored by lack of progress, but maybe some additive combinatorialists here know further. I'm not claiming it is conceptual or ...
- 33.8k