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SUMMARY:Alexander Clifton (Emory University)
DTSTART:20210215T133000Z
DTEND:20210215T140000Z
DTSTAMP:20260423T021234Z
UID:POINT/28
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/POINT/28/">A
 n exponential bound for exponential diffsequences</a>\nby Alexander Clifto
 n (Emory University) as part of POINT: New Developments in Number Theory\n
 \n\nAbstract\nA theorem of van der Waerden states that for any positive in
 teger $r$\, if you partition $\\mathbf{N}$ into $r$ disjoint subsets\, the
 n one of them will contain arbitrarily long arithmetic progressions. It is
  natural to ask what other arithmetic structures are preserved when partit
 ioning $\\mathbf{N}$ into a finite number of disjoint sets and to pose qua
 ntitative questions about these. We consider $D$-diffsequences\, introduce
 d by Landman and Robertson\, which are increasing sequences in which the c
 onsecutive differences all lie in some given set $D$. Here\, we consider t
 he case where $D$ consists of all powers of $2$ and define $f(k)$ to be th
 e smallest $n$ such that partitioning $\\{1\,2\,\\cdots\,n\\}$ into $2$ su
 bsets guarantees the presence of a $D$-diffsequence of length $k$ containe
 d entirely within one subset. We establish that $f(k)$ grows exponentially
 .\n
LOCATION:https://researchseminars.org/talk/POINT/28/
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