Treffer: The main zero-sum constants over $D_{2n} \times C_2$: The main zero-sum constants over \(D_{2n}\times C_2\)
Title:
The main zero-sum constants over $D_{2n} \times C_2$: The main zero-sum constants over \(D_{2n}\times C_2\)
Authors:
Publication Status:
Preprint
Publisher Information:
arXiv, 2021.
Publication Year:
2021
Subject Terms:
small Davenport constant, Mathematics - Number Theory, Inverse problems of additive number theory, including sumsets, 11B75, 11B50, 11P70, \(\eta\)-constant, Erdős-Ginzburg-Ziv constant, Sequences (mod \(m\)), Gao constant, zero-sum problem, Other combinatorial number theory, FOS: Mathematics, Mathematics - Combinatorics, Number Theory (math.NT), Combinatorics (math.CO), Gao's conjecture
Document Type:
Fachzeitschrift
Article
File Description:
application/xml
DOI:
10.48550/arxiv.2108.00823
DOI:
10.1137/22m1496013
Access URL:
Rights:
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....ceebaa0a92049e6bacf0396cf6280fd9
Database:
OpenAIRE
Weitere Informationen
Let $C_2$ be the cyclic group of order $2$ and $D_{2n}$ be the dihedral group of order $2n$, where $n$ is even. In this paper, we provide the exact values of some zero-sum constants over $D_{2n} \times C_2$, namely small Davenport constant, Gao constant, $��$-constant and Erd\H os-Ginzburg-Ziv constant. As a consequence, we prove the Gao's and Zhuang-Gao's Conjectures for this group. These are the first concrete results on zero-sum problems for a family of non-abelian groups of rank greater than $2$.
12 pages