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SUMMARY:Kaimin Cheng (China West Normal University)
DTSTART:20261006T120000Z
DTEND:20261006T130000Z
DTSTAMP:20260915T102149Z
UID:OWNS/171
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/171/">F
 rom Cusick's conjecture to deletion rigidity in binary digit problems</a>\
 nby Kaimin Cheng (China West Normal University) as part of One World Numer
 ation seminar\n\n\nAbstract\nLet $s_2(n)$ denote the sum of the binary dig
 its of $n$. Cusick's conjecture asserts that for every positive integer $t
 $\, $\\mathrm{dens}\\{n \\ge 0: s_2(n+t) \\ge s_2(n)\\} > 1/2$. In this ta
 lk\, I will present a proof based on a first-exit interpretation of binary
  addition\, in which the relevant distributions are realized through stopp
 ed random walks on subsequence ideals of binary words. I will then briefly
  discuss extensions of this viewpoint to the Tu–Deng conjecture\, cyclic
  deletion rigidity and Macaulay shadows\, as well as sharp extremal asympt
 otics for Cusick's bias at fixed Hamming weight.\n
LOCATION:https://researchseminars.org/talk/OWNS/171/
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