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SUMMARY:Filip Gawron (Jagiellonian University\, Poland)
DTSTART:20220527T173000Z
DTEND:20220527T175500Z
DTSTAMP:20260423T011437Z
UID:CANT2022/51
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/51/
 ">Sign behavior of sums of weighted numbers of partitions</a>\nby Filip Ga
 wron (Jagiellonian University\, Poland) as part of Combinatorial and addit
 ive number theory (CANT 2022)\n\n\nAbstract\nLet $A$ be a subset of the po
 sitive integers. By an $A$-partition of $n$ we\nunderstand the representat
 ion of $n$ as a sum of elements from the set $A$. For\ngiven $i$\, $n\\in 
 \\mathbb{N}$\, by $c_A(i\,n)$ we denote the number of $A$-partitions of $n
 $ with\nexactly $i$ parts. In the talk I will describe several results con
 cerning the sign behaviour\nof the sequence $S_{A\,k}(n) = \\sum_{i=0}^n(-
 1)^i i^k c_A(i\, n)$\, for fixed $k\\in \\mathbb{N}$.   I will focus on th
 e periodicity of the sequence of signs for different forms of $A$. Finally
 \, I will also mention some conjectures and questions that arose naturally
  during our research.\n\nThe talk is based on a joint work with Maciej Ula
 s (Jagiellonian University).\n
LOCATION:https://researchseminars.org/talk/CANT2022/51/
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