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SUMMARY:Aritram Dhar (University of Florida)
DTSTART:20250520T210000Z
DTEND:20250520T212500Z
DTSTAMP:20260423T041812Z
UID:CANT2025/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/26/
 ">A bijective proof of an identity of Berkovich and Uncu</a>\nby Aritram D
 har (University of Florida) as part of Combinatorial and additive number t
 heory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center
  (4th floor).\n\nAbstract\nThe BG-rank BG($\\pi$) of an integer partition 
 $\\pi$ is defined as $$\\text{BG}(\\pi) := i-j$$ where $i$ is the number o
 f odd-indexed odd parts and $j$ is the number of even-indexed odd parts of
  $\\pi$. In a recent work\, Fu and Tang ask for a direct combinatorial pro
 of of the following identity of Berkovich and Uncu $$B_{2N+\\nu}(k\,q)=q^{
 2k^2-k}\\left[\\begin{matrix}2N+\\nu\\\n+k\\end{matrix}\\right]_{q^2}$$ fo
 r any integer $k$ and non-negative integer $N$ where $\\nu\\in \\{0\,1\\}$
 \, $B_N(k\,q)$ is the generating function for partitions into distinct par
 ts less than or equal to $N$ with BG-rank equal to $k$ and $\\left[\\begin
 {matrix}a+b\\\\b\\end{matrix}\\right]_q$ is a Gaussian binomial coefficien
 t. In this talk\, I will give a bijective proof of Berkovich and Uncu's id
 entity along the lines of Vandervelde and Fu and Tang's idea. \nThis is jo
 int work with Avi Mukhopadhyay.\n
LOCATION:https://researchseminars.org/talk/CANT2025/26/
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