BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Krystian Gajdzica (Jagiellonian University\, Poland)
DTSTART:20260718T133000Z
DTEND:20260718T135500Z
DTSTAMP:20260710T111453Z
UID:CANT2026/79
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/79/
 ">On the Bessenrodt-Ono inequality for polynomials</a>\nby Krystian Gajdzi
 ca (Jagiellonian University\, Poland) as part of Combinatorial and additiv
 e number theory seminar (CANT 2026)\n\nLecture held in Science Center in t
 he CUNY Graduate Center (4th floor).\n\nAbstract\nIn 2016\, Bessenrodt and
  Ono proved that the partition function satisfies the inequality $\n p(a)p
 (b)>p(a+b)\n$\nfor all $a\,b\\geqslant2$ with $a+b>9$. Since then\, analog
 ous properties have been investigated for many partition statistics. In th
 is talk\, following Gian-Carlo Rota's advice\, we move from the discrete p
 roblem to the continuous one\, and consider a family of recursively define
 d polynomials \n$\nP_n^g(x) := \\frac{x}{n} \\sum_{k=1}^n g(k) P_{n-k}^g(x
 )\n$\nwith the initial condition $P_0^g(x):=1$\, where $(g(n))_{n\\in\\mat
 hbb{N}}$ is an arbitrary sequence of positive real numbers such that $g(1)
 =1$. We derive an efficient criterion characterizing when the inequality \
 n$\n P_{a}^g(x)P_{b}^g(x)\\geqslant P_{a+b}^g(x)\n$\n is satisfied for all
  $x\\geqslant x_0$ and $a\,b\\geqslant1$\, where $x_0$ is some real number
  depending on $g$.  Moreover\, we illustrate the usefulness of this criter
 ion by applying it to various combinatorial sequences.\n
LOCATION:https://researchseminars.org/talk/CANT2026/79/
END:VEVENT
END:VCALENDAR