BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Piotr Miska (Jagiellonian University\, Krakow\, Poland)
DTSTART:20220525T173000Z
DTEND:20220525T175500Z
DTSTAMP:20260423T011438Z
UID:CANT2022/23
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/23/
 ">On (non-)realizibility of Stirling numbers</a>\nby Piotr Miska (Jagiello
 nian University\, Krakow\, Poland) as part of Combinatorial and additive n
 umber theory (CANT 2022)\n\n\nAbstract\nWe say that a sequence $(a_n)_{n\\
 in\\mathbb{N}_+}$ of non-negative integers is realizable if there exists a
  set $X$ and a mapping $T : X \\to X$ such that $a_n$ is the number of fix
 ed points of $T^n$. For each $k \\in\\mathbb{N}_+$ and $j \\in \\{1\,2\\}$
  we define a sequence $S^{(j)}_k =(S^{(j)}(n+k -1\,k))_{n\\in\\mathbb{N}_+
 }$ \, where $S^{(j)}(n\,k)$ is the Stirling number of the $j$-th kind (in 
 case of $j = 1$ we consider unsigned Stirling numbers). The aim of the tal
 k is to prove that $S^{(2)}_k$ is realizable if and only if $k \\in \\{1\,
 2\\}$\, while for $k \\geq 3$ the sequence $S^{(2)}_k$ is almost realizabl
 e with a failure $(k-1)!$\, i. e. $(k-1)!S^{(2)}_k$ is realizable. Moreove
 r\, I will show that for each $k \\in\\mathbb{N}_+$ the sequence $S^{(1)}_
 k$ is not almost realizable\, i. e. for any $r \\in\\mathbb{N}_+$ the sequ
 ence $rS^{(1)}_k$ is not realizable. \n\nThe talk is based on a joint work
  with Tom Ward (Newcastle\, UK).\n
LOCATION:https://researchseminars.org/talk/CANT2022/23/
END:VEVENT
END:VCALENDAR