Representation of finite abelian group elements by subsequence sums

Representation of Finite Abelian Group Elements by Subsequence Sums

Let G ∼= Cn1 ⊕ · · · ⊕ Cnr be a finite and nontrivial abelian group with n1|n2| . . . |nr. A conjecture of Hamidoune says that if W = w1 · · ·wn is a sequence of integers, all but at most one relatively prime to |G|, and S is a sequence over G with |S| ≥ |W |+ |G| − 1 ≥ |G| + 1, the maximum multiplicity of S at most |W |, and σ(W ) ≡ 0 mod |G|, then there exists a nontrivial subgroup H such tha...

Subsequence Sums of Zero-sum Free Sequences over Finite Abelian Groups

Let G be a finite abelian group of rank r and let X be a zero-sum free sequence over G whose support supp(X) generates G. In 2009, Pixton proved that |Σ(X)| ≥ 2r−1(|X| − r + 2) − 1 for r ≤ 3. In this paper, we show that this result also holds for abelian groups G of rank 4 if the smallest prime p dividing |G| satisfies p ≥ 13.

Counting subset sums of finite abelian groups

In this paper, we obtain an explicit formula for the number of zero-sum k-element subsets in any finite abelian group.

Spanning Subset Sums for Finite Abelian

Finite Abelian Groups and Character Sums

These are some notes I have written up for myself. I have compiled what I feel to be some of the most important facts concerning characters on finite abelian groups, especially from a number theoretic point of view. I decided to distribute these because I couldn’t find a single reference that covered everything that I thought was relevant to the material I will discuss on Wednesday. Of course, ...