Some recent results on Wilf's conjecture

Abstract: A numerical semigroup is a submonoid $S$ of the nonnegative integers with finite complement. Its \emph{conductor} is the smallest integer $c \ge 0$ such that $S$ contains all integers $z \ge c$, and its \emph{left part} $L$ is the set of all $s \in S$ such that $s < c$. In 1978, Wilf asked whether the inequality $n|L| \ge c$ always holds, where $n$ is the least number of generators of $S$. This is now known as Wilf's conjecture. In this talk, we present some recent results towards it, using tools from commutative algebra and graph theory.

number theory

Audience: researchers in the topic

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.