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pro vyhledávání: '"Grynkiewicz, David J."'
Autor:
Grynkiewicz, David J.
The $3k-4$ Theorem asserts that, if $A,\,B\subseteq \mathbb Z$ are finite, nonempty subsets with $|A|\geq |B|$ and $|A+B|=|A|+|B|+r< |A|+2|B|-3$, then there are arithmetic progressions $P_A$ and $P_B$ of common difference with $X\subseteq P_X$ with $
Externí odkaz:
http://arxiv.org/abs/2402.15028
Autor:
Ebert, John, Grynkiewicz, David J.
Let $G=(\mathbb Z/n\mathbb Z) \oplus (\mathbb Z/n\mathbb Z)$. Let $\mathsf {s}_{\leq k}(G)$ be the smallest integer $\ell$ such that every sequence of $\ell$ terms from $G$, with repetition allowed, has a nonempty zero-sum subsequence with length at
Externí odkaz:
http://arxiv.org/abs/2211.08515
Autor:
Grynkiewicz, David J.
We begin by explaining how arguments used by R. Wilson to give an elementary proof of the $\mathbb F_p$ case for the Ax-Katz Theorem can also be used to prove the following generalization of the Chevalley-Warning and Ax-Katz Theorems for $\mathbb F_p
Externí odkaz:
http://arxiv.org/abs/2208.12895
Autor:
Grynkiewicz, David J., Liu, Chao
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 length at most $mn+n-1-k$. The associated inverse question is to character
Externí odkaz:
http://arxiv.org/abs/2109.10309
Autor:
Grynkiewicz, David J.
The Davenport constant for a finite abelian group $G$ is the minimal length $\ell$ such that any sequence of $\ell$ terms from $G$ must contain a nontrivial zero-sum sequence. For the group $G=(\mathbb Z/n\mathbb Z)^2$, its value is $2n-1$, which is
Externí odkaz:
http://arxiv.org/abs/2107.10619
Autor:
Ebert, John J., Grynkiewicz, David J.
Publikováno v:
In European Journal of Combinatorics May 2024 118
Autor:
Grynkiewicz, David J.
Our motivating goal is factorization in Krull Domains $H$ with finitely generated class group $G$. The elasticity $\rho(H)$ is the maximal number of atoms in any re-factorization of a product of $k$ atoms. The elasticities are the same as those of a
Externí odkaz:
http://arxiv.org/abs/2012.12757
Autor:
Grynkiewicz, David J.
The $3k-4$ Theorem is a classical result which asserts that if $A,\,B\subseteq \mathbb Z$ are finite, nonempty subsets with \begin{equation}\label{hyp}|A+B|=|A|+|B|+r\leq |A|+|B|+\min\{|A|,\,|B|\}-3-\delta,\end{equation} where $\delta=1$ if $A$ and $
Externí odkaz:
http://arxiv.org/abs/1911.12858