Additive bases in infinite abelian semigroups, II

Abstract: This talk is a continuation of part I by Pierre-Yves Bienvenu, though it will be self-contained. Let $T$ be a semigroup and $A$ be a basis $T$. If $F$ is a finite subset of $A$ and $A \setminus F $ is still a basis $T$ (of a possibly different order), can we bound the order of $A \setminus F$ in terms of that of $A$ and $|F|$? In the semigroup $\mathbf{N}$, this question was first studied by Erd\H{o}s and Graham when $F$ is a singleton, and by Nash and Nathanson for general $F$. We prove a general bound for all translatable semigroups. Besides studying the maximum order of $A \setminus F$, we also study its "typical" order.

Joint work with Pierre-Yves Bienvenu and Benjamin Girard.

number theory

Audience: researchers in the topic

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Combinatorial and additive number theory (CANT 2021)

Series comments: This is the nineteenth in a series of annual workshops sponsored by the New York Number Theory Seminar on problems in combinatorial and additive number theory and related parts of mathematics.

Registration for the conference is free. Register at cant2021.eventbrite.com.

The conference website is www.theoryofnumbers.com/cant/ Lectures will be broadcast on Zoom. The Zoom login will be emailed daily to everyone who has registered on eventbrite. To join the meeting, you may need to download the free software from www.zoom.us.

The conference program, list of speakers, and abstracts are posted on the external website.

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