D. Grynkiewicz

most citedWeighted Sequences in Finite Cyclic Groups

5 citations · 9 across the 7 of their papers we have counts for

collaborators

7 papers

math.NT2008★ 3 cited

Representation of Finite Abelian Group Elements by Subsequence Sums

D. J. Grynkiewicz, E. Marchan, O. Ordaz

Let $G ≅ C_{n_{1}} \oplus ... \oplus C_{n_{r}}$ be a finite and nontrivial abelian group with $n_{1} ∣ n_{2} ∣...∣ n_{r}$ . A conjecture of Hamidoune says that if $W = w_{1} ... w_{n}$ is a sequence o…

math.NT2008

On Extending Pollard's Theorem for t-Representable Sums

David J. Grynkiewicz

Let $t \geq 1$ , let $A$ and $B$ be finite, nonempty subsets of an abelian group $G$ , and let $A\pp{i} B$ denote all the elements $c$ with at least $i$ representations of the form $c…

math.NT2008

Inverse Zero-Sum Problems III

Weidong Gao, Alfred Geroldinger, David J. Grynkiewicz

Let $G$ be a finite abeilian group. A sequence $S$ with terms from $G$ is zero-sum if the sum of terms in $S$ equals zero. It is a minimal zero-sum sequence if no proper, nontrivia…

math.CO2007★ 5 cited

Weighted Sequences in Finite Cyclic Groups

David J. Grynkiewicz, Jujuan Zhuang

Let $p > 7$ be a prime, let $G = Z / p Z$ , and let $S_{1} = \prod_{i = 1}^{p} g_{i}$ and $S_{2} = \prod_{i = 1}^{p} h_{i}$ be two sequences with terms from $G$ . Suppose that the maximum multiplicity of a t…

math.CO2007

Properties of two dimensional sets with small sumset

David J. Grynkiewicz, Oriol Serra

Let $A, B \subseteq R^{2}$ be finite, nonempty subsets, let $s \geq 2$ be an integer, and let $h_{1} (A, B)$ denote the minimal number $t$ such that there exist $2 t$ (not necessar…

math.CO2007

Connectivity of Addition Cayley Graphs

David J. Grynkiewicz, Oriol Serra, Vsevolod Lev

For any finite abelian group $G$ and any subset $S\seq G$, we determine the connectivity of the addition Cayley graph induced by $S$ on $G$ . Moreover, we show that if this graph is…