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SUMMARY:A Ramsey Characterisation of Eventually Perioidic Words - Maria Iv
 an (Cambridge)
DTSTART:20240125T143000Z
DTEND:20240125T153000Z
UID:TALK211282@talks.cam.ac.uk
CONTACT:103978
DESCRIPTION:A factorisation x = u1 u2 · · · of an infinite word x on al
 pha-\nbet X is called ‘super-monochromatic’\, for a given colouring of
  the finite\nwords X∗ on alphabet X\, if each word uk1 uk2 · · · ukn 
 \, where k1 < · · · < kn\,\nis the same colour. A direct application of
  Hindman’s theorem shows that\nif x is eventually periodic\, then for ev
 ery finite colouring of X∗\, there ex-\nist a suffix of x that admits a 
 super-monochromatic factorisation. What\nabout the converse?\nIn this talk
  we show that the converse does indeed hold: thus a word\nx is eventually 
 periodic if and only if for every finite colouring of X∗\nthere is a suf
 fix of x having a super-monochromatic factorisation. This\nhas been a conj
 ecture in the community for some time. Our main tool\nis a Ramsey result a
 bout alternating sums. This provides a strong link\nbetween Ramsey theory 
 and the combinatorics of infinite words.\nJoint work with Imre Leader and 
 Luca Q. Zamboni
LOCATION:MR12
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