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arXiv · 2204.08392

Quasihomomorphisms from the integers into Hamming metrics

Jan Draisma·Rob H. Eggermont·Tim Seynnaeve·Nafie Tairi·Emanuele Ventura
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Abstract

A function $f: \mathbb{Z} \to \mathbb{Q}^n$ is a $c$-quasihomomorphism if the Hamming distance between $f(x+y)$ and $f(x)+f(y)$ is at most $c$ for all $x,y \in \mathbb{Z}$. We show that any $c$-quasihomomorphism has distance at most some constant $C(c)$ to an actual group homomorphism; here $C(c)$ depends only on $c$ and not on $n$ or $f$. This gives a positive answer to a special case of a question posed by Kazhdan and Ziegler.

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Jan Draisma, Rob H. Eggermont, Tim Seynnaeve, Nafie Tairi, Emanuele Ventura. 2022-04-18. Quasihomomorphisms from the integers into Hamming metrics. https://arxiv.org/abs/2204.08392

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