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SUMMARY:Johann Thiel (New York City College of Technology (CUNY))
DTSTART:20250522T193000Z
DTEND:20250522T195500Z
DTSTAMP:20260423T024835Z
UID:CANT2025/48
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/48/
 ">Bivariate polynomials associated with binary trees created by QuickSort<
 /a>\nby Johann Thiel (New York City College of Technology (CUNY)) as part 
 of Combinatorial and additive number theory (CANT 2025)\n\nLecture held in
  CUNY Graduate Center - Science Center (4th floor).\n\nAbstract\nIn this t
 alk we describe a generating series whose coefficients are polynomials tha
 t\, for a given positive integer $n$\, encode the depth at which the vario
 us list entries appear as labeled nodes in the binary trees obtained by Qu
 ickSorting permutations of the list consisting of one copy of each of the 
 first $n$ non-negative integers. Extracting the appropriate coefficients y
 ields information for the number of times a given list entry appears at a 
 given depth\, the total number of list entries that appear at a given dept
 h\, and consequently the average number of list entries that appear at a g
 iven depth taken over all $n!$ permutations. Joint work with David M. Brad
 ley.\n
LOCATION:https://researchseminars.org/talk/CANT2025/48/
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