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UID:5893@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20221107T150000
DTEND;TZID=Europe/Paris:20221107T160000
DTSTAMP:20241120T200649Z
URL:https://www.i2m.univ-amu.fr/evenements/q-recursive-sequences-and-their
 -asymptotic-analysis/
SUMMARY:Daniel Krenn (Paris Lodron University of Salzburg): q-recursive seq
 uences and their asymptotic analysis
DESCRIPTION:Daniel Krenn: In this talk\, we consider Stern’s diatomic seq
 uence\, the number of non-zero elements in some generalized Pascal's trian
 gle and the number of unbordered factors in the Thue-Morse sequence as run
 ning examples. All these sequences can be defined recursively and lead to 
 the concept of so-called qqq-recursive sequences. Here qqq is an integer a
 nd at least 222\, and qqq-recursive sequences are sequences which satisfy 
 a specific type of recurrence relation: Roughly speaking\, every subsequen
 ce whose indices run through a residue class modulo qMq^MqM is a linear co
 mbination of subsequences where for each of these subsequences\, the indic
 es run through a residue class modulo qmq^mqm for some m&lt\;Mm &lt\; Mm&l
 t\;M.\nIt turns out that this property is quite natural and many combinato
 rial sequences are in fact qqq-recursive. We will see that qqq-recursive s
 equences are related to qqq-regular sequences and a qqq-linear representat
 ion of a sequence can be computed easily. Our main focus is the asymptotic
  behavior of the summatory functions of qqq-recursive sequences. Beside ge
 neral results\, we present a precise asymptotic analysis of our three exam
 ples. For the first two sequences\, our analysis even leads to precise for
 mulae without error terms.\nhttps://www.youtube.com/watch?v=U4AjnSWhQMY\n\
 n\n\nThe address of the Zoom meeting is https://zoom.us/j/92245493528 . Th
 e password is distributed in announcements. If you want to receive them\, 
 or receive them and want to unsubscribe\, please write to Anna Frid.\nMore
  info: https://www.i2m.univ-amu.fr/wiki/Combinatorics-on-Words-seminar/
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 022/10/Daniel_Krenn-2019.jpg
CATEGORIES:Combinatorics on Words Seminar
LOCATION:Virtual event\, visioconférence\, virtual\, France
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 , France;X-APPLE-RADIUS=100;X-TITLE=Virtual event:geo:0,0
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