Restricted multicompositions

Abstract: In 2007, George Andrews introduced $k$-compositions, a generalization of integer compositions, where each summand has $k$ possible colors, except for the final part which must be color 1. Last year, St\'ephane Ouvry and Alexios Polychronakos introduced $g$-compositions which allow for up to $g-2$ zeros between parts. Although these do not have the same definition and came from very different motivations (number theory and quantum mechanics, respectively), we will see that they are equivalent. One reason these are compelling combinatorial objects is their count: there are $(k+1)^{n-1}$ $k$-compositions of $n$. Results from standard integer compositions can have interesting generalizations. For example, there are three types of restricted compositions counted by Fibonacci numbers---parts 1 & 2, odd parts, and parts greater than 1. We will explore the diverging families of recurrences that arise from applying these restrictions to multicompositions.

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.