Évènement

Daniel Krenn
Paris Lodron University of Salzburg
https://www.danielkrenn.at/

Date(s) : 07/11/2022   iCal
15h00 - 16h00

In this talk, we consider Stern’s diatomic sequence, the number of non-zero elements in some generalized Pascal’s triangle and the number of unbordered factors in the Thue-Morse sequence as running examples. All these sequences can be defined recursively and lead to the concept of so-called $q$-recursive sequences. Here $q$ is an integer and at least $2$, and $q$-recursive sequences are sequences which satisfy a specific type of recurrence relation: Roughly speaking, every subsequence whose indices run through a residue class modulo qMq^MqM is a linear combination of subsequences where for each of these subsequences, the indices run through a residue class modulo qmq^mqm for some $m<M$.

It turns out that this property is quite natural and many combinatorial sequences are in fact $q$-recursive. We will see that $q$-recursive sequences are related to $q$-regular sequences and a $q$-linear representation of a sequence can be computed easily. Our main focus is the asymptotic behavior of the summatory functions of $q$-recursive sequences. Beside general results, we present a precise asymptotic analysis of our three examples. For the first two sequences, our analysis even leads to precise formulae without error terms.

The address of the Zoom meeting is https://zoom.us/j/92245493528 . The password is distributed in announcements. If you want to receive them, or receive them and want to unsubscribe, please write to Anna Frid.
More info: https://www.i2m.univ-amu.fr/wiki/Combinatorics-on-Words-seminar/

Emplacement
Virtual event

Catégories Pas de Catégories