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SUMMARY:Jinhui Fang (Nanjing Normal University\, Nanjing\, China)
DTSTART:20260715T133000Z
DTEND:20260715T135500Z
DTSTAMP:20260710T111435Z
UID:CANT2026/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/32/
 ">Minimal asymptotic bases related to G-adic sequences</a>\nby Jinhui Fang
  (Nanjing Normal University\, Nanjing\, China) as part of Combinatorial an
 d additive number theory seminar (CANT 2026)\n\nLecture held in Science Ce
 nter in the CUNY Graduate Center (4th floor).\n\nAbstract\nLet $A$ be a se
 t of nonnegative integers and $h\\ge 2$. The set $A$ is defined as an asym
 ptotic basis of order $h$ if all sufficiently large integers $n$ can be ex
 pressed as the sum of $h$ elements taken from $A$. Such $A$ is further def
 ined as \\emph{minimal} if no proper subset of $A$ is an asymptotic basis 
 of order $h$. In 1974\, Nathanson explicitly constructed a minimal asympto
 tic basis of order $2$ by using binary representations. In 2022\, Nathanso
 n constructed a new class of minimal asymptotic bases of order $h$ based o
 n the $\\mathcal{G}$-adic sequence\, where a $\\mathcal{G}$-adic sequence 
 $\\mathcal{G}=\\{g_i\\}_{i=0}^{\\infty}$ is a strictly increasing sequence
  of positive integers such that $g_0=1$ and $g_{i-1}$ divides $g_i$ for al
 l $i\\ge 1$. Recently\, we improve the above result.\n
LOCATION:https://researchseminars.org/talk/CANT2026/32/
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