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SUMMARY:Infinite monochromatic exponential patterns - Mariaclara Ragosta (
 Pisa)
DTSTART:20240201T143000Z
DTEND:20240201T153000Z
UID:TALK211369@talks.cam.ac.uk
CONTACT:103978
DESCRIPTION:Schur's Theorem (1916) states that for every finite coloring o
 f $\n$ there\nexists a monochromatic triple $a\, b\, a+b$. Several decades
  later\, Folkman\nextended this statement by including in a same color arb
 itrarily long\nsequences and all finite sums from them. A breakthrough was
  made in 1974 by\nHindman\, who showed\, in the same setting\, the existen
 ce of an\ninfinite sequence such that all finite sums are monochromatic\, 
 and one year\nlater the theorem was extended to all associative operations
 .\nIn this talk we explore the case of exponentiation\, first investigated
  by\nSisto (2011) and recently by Sahasrabudhe (2018). The latter proved a
  \noFolkman Theorem for product and exponentiation at the same time. In ou
 r\nmain theorem we realise for exponentiation the passage from finite to\n
 infinite made by Hindman for sums\, by showing that for every finite\ncolo
 ring of $\n$ there exists an infinite sequence such that all finite\nexpon
 entiations are monochromatic.\nWe also extend the theorem to a larger clas
 s of binary non-associative\noperations which somehow behave in the same m
 anner as exponentiation.\nThis is joint work with Mauro Di Nasso.
LOCATION:MR12
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