D. Grynkiewicz

activity

20072026

most citedThe Catenary Degree of Krull Monoids I

32 citations · 83 across the 32 of their papers we have counts for

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26 papers · 1 filter

math.NT2026

Pollard's theorem in general abelian groups

David J. Grynkiewicz, Runze Wang

We make further progress towards a Kneser-type generalization of Pollard's Theorem to general abelian groups. For two sets $A$ and $B$ in an abelian group $G$ , the \emph{ $t$ -popula…

math.NT2024

The $3 k - 4$ Theorem modulo a Prime: High Density for $A + B$

David J. Grynkiewicz

The $3 k - 4$ Theorem asserts that, if $A, B \subseteq Z$ are finite, nonempty subsets with $∣ A ∣ \geq ∣ B ∣$ and $∣ A + B ∣ = ∣ A ∣ + ∣ B ∣ + r < ∣ A ∣ + 2∣ B ∣ - 3$ , then there are arithmetic progress…

math.NT2022

Structure of a sequence with prescribed zero-sum subsequences: Rank Two $p$ -groups

John Ebert, David J. Grynkiewicz

Let $G = (Z / n Z) \oplus (Z / n Z)$ . Let $s_{\leq k} (G)$ be the smallest integer $ℓ$ such that every sequence of $ℓ$ terms from $G$ , with r…

math.NT2022

A Generalization of the Chevalley-Warning and Ax-Katz Theorems with a View Towards Combinatorial Number Theory

David J. Grynkiewicz

We begin by explaining how arguments used by R. Wilson to give an elementary proof of the $F_{p}$ case for the Ax-Katz Theorem can also be used to prove the following general…

math.NT2021

A Multiplicative Property for Zero-Sums II

David J. Grynkiewicz, Chao Liu

Let $G = C_{n} \oplus C_{mn}$ with $n \geq 2$ and $m \geq 1$ , and let $k \in [0, n - 1]$ . It is known that any sequence of $mn + n - 1 + k$ terms from $G$ must contain a nontrivial zero-sum of leng…

math.NT2021

A Multiplicative Property for Zero-Sums I