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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

3 votes
1 answer
164 views

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 …
0 votes
0 answers
159 views

One-product free sequences for $A_n$

I am working on computing the Davenport constant $D(G)$ for $S_n$ and $A_n$, i.e., the minimal number $d$ such that every sequence (multiset) of $d$ elements contains some subsequence giving identity …
2 votes
1 answer
223 views

Is the small Davenport constant for $S_n$, $d(S_n)=n(n-1)/2$?

The Davenport constant $D(G)$ of a finite group $G$ is the minimal $d$ such that any sequence/multiset of length $d$ is one-product, i.e., identity can be obtained as a product (in some order) of some …
3 votes
1 answer
252 views

Davenport constant $D(S_5)=10$ or $11$?

I am working on computing the Davenport constant $D(G)$ of symmetric groups, which is the minimal number $d$ such that every sequence of $d$ elements, possibly with repetitions, is one-product, i.e. t …
3 votes
0 answers
152 views

Correspondence between even and odd permutations in $S_5$

I am working on the Davenport constant for symmetric groups, $D(G)$ , which is the minimal number $d$ such that every sequence of $d$ elements in the group G is one-product sequence, i.e, we can alway …