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SUMMARY:Steven Senger (Missouri State University)
DTSTART:20250522T203000Z
DTEND:20250522T205500Z
DTSTAMP:20260423T024829Z
UID:CANT2025/50
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/50/
 ">VC-dimension of subsets of the Hamming graph</a>\nby Steven Senger (Miss
 ouri State University) as part of Combinatorial and additive number theory
  (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center (4th
  floor).\n\nAbstract\nVapnik-Chervonenkis or VC-dimension has been a usefu
 l tool in combinatorics\, machine learning\, and other areas. Given a grap
 h from a well-studied family\, there has been recent activity on size thre
 sholds for a subset of a graph to guarantee bounds on the VC-dimension of 
 the subset. These resemble finite point configuration results\, such as th
 e Erdos-Falconer distance problem\, both in form as well as in the techniq
 ues of proof. Typically\, one looks at graphs that are highly pseudorandom
 \, such as the distance graph or the dot product graph\, but the Hamming g
 raph is quantifiably less pseudorandom\, and standard techniques seem to b
 reak down and yield very weak results if any. We present a suite of result
 s that outperform their counterparts for the Hamming graph. The proofs are
  completely elementary\, and in some cases\, tight.\n
LOCATION:https://researchseminars.org/talk/CANT2025/50/
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