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SUMMARY:Fei Peng (Carnegie Mellon University)
DTSTART:20200605T160000Z
DTEND:20200605T162500Z
DTSTAMP:20260423T011158Z
UID:CANT2020/73
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/73/
 ">Distribution of missing differences in diffsets</a>\nby Fei Peng (Carneg
 ie Mellon University) as part of Combinatorial and additive number theory 
 (CANT 2021)\n\n\nAbstract\nLazarev\, Miller\, and O'Bryant investigated th
 e distribution of $|S+S|$\nfor $S$ chosen uniformly at random from $\\{0\,
  1\, \\dots\, n-1\\}$\, and proved the existence\nof a divot at missing 7 
 sums (the probability of missing exactly 7 sums is less than\nmissing 6 or
  missing 8 sums). We study related questions for $|S-S|$\, and show some d
 ivots\nfrom one end of the probability distribution\, $P(|S-S|=k)$\, as we
 ll as a peak at $k=4$\nfrom the other end\, $P(2n-1-|S-S|=k)$. A corollary
  of our results is an asymptotic bound\nfor the number of complete rulers 
 of length $n$.\nJoint with Scott Harvey-Arnold and Steven J. Miller.\n
LOCATION:https://researchseminars.org/talk/CANT2020/73/
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