A stronger connection between the Erdős-Burgess and Davenport constants
Abstract
The Erdős-Burgess constant of a semigroup $S$ is the smallest positive integer $k$ such that any sequence over $S$ of length $k$ contains a nonempty subsequence whose elements multiply to an idempotent element of $S$. In the case where $S$ is the multiplicative semigroup of $\mathbb{Z}/n\mathbb{Z}$, we confirm a conjecture connecting the Erdős-Burgess constant of $S$ and the Davenport constant of $(\mathbb{Z}/n\mathbb{Z})^{\times}$ for $n$ with at most two prime factors. We also discuss the extension of our techniques to other rings.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2018
- DOI:
- 10.48550/arXiv.1808.06031
- arXiv:
- arXiv:1808.06031
- Bibcode:
- 2018arXiv180806031K
- Keywords:
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- Mathematics - Combinatorics