BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//wp-events-plugin.com//7.2.3.1//EN
TZID:Europe/Paris
X-WR-TIMEZONE:Europe/Paris
BEGIN:VEVENT
UID:8299@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20140916T110500
DTEND;TZID=Europe/Paris:20140916T120000
DTSTAMP:20241120T210328Z
URL:https://www.i2m.univ-amu.fr/evenements/additive-combinatorics-generate
 d-by-uniformly-recurrent-words/
SUMMARY:Svetlana Puzynina (Sobolev Institute of Mathematics\, Novosibirsk\,
  Russia): Additive combinatorics generated by uniformly recurrent words
DESCRIPTION:Svetlana Puzynina: A subset A of the set N of natural numbers i
 s called an IP-set if A contains all finite sums of distinct terms of some
  infinite sequence of natural numbers. We show how certain families of ape
 riodic words of low factor complexity may be used to generate a wide assor
 tment of IP-sets having additional nice properties inherited from the rich
  combinatorial structure of the underlying word. We consider Sturmian word
 s and their extensions to larger alphabets (so-called Arnoux-Rauzy words)\
 , as well as words generated by substitution rules. Our methods simultaneo
 usly exploit the general theory of combinatorics on words\, the arithmetic
  properties of abstract numeration systems defined by substitution rules\,
  notions from topological dynamics including proximality and equicontinuit
 y\, and the beautiful and elegant theory\, developed by N. Hindman\, D. St
 rauss and others\, linking IP-sets to the algebraic/topological properties
  of the Stone-Cech compactification of N.\nTogether with the property of b
 eing IP-set\, we consider two related additive properties of subsets of po
 sitive integers: We say that a subset A of N is finite (resp.\, infinite) 
 FS-big if for each positive integer k the set A contains finite sums with 
 at most k summands of some k-term (resp.\, infinite) sequence of natural n
 umbers. By a celebrated result of Hindman (1974)\, the collection of all I
 P-sets is partition regular\, i.e.\, if A is an IP-set\, then for any fini
 te partition of A\, one cell of the partition is an IP-set. We prove that 
 the collection of all finite FS-big sets is also partition regular. Using 
 the Thue-Morse word we show that the collection of all infinite FS-big set
 s is not partition regular. The talk is based on joint work with M. Bucci\
 , N. Hindman\, L. Q. Zamboni.\nReferences\nM. Bucci\, S. Puzynina\, L. Q. 
 Zamboni\, Central sets generated by uniformly recurrent words\, To appear 
 in Ergodic Theory and Dynamical Systems. doi:10.1017/etds.2013.69\nM. Bucc
 i\, N. Hindman\, S. Puzynina\, L. Q. Zamboni Additive properties of sets d
 efined by the Thue-Morse word. Journal of Combinatorial Theory\, Series A\
 , 120 (2013)\, 1235--1245.\nN. Hindman and D. Strauss\, Algebra in the Sto
 ne-Cech compactification: theory and applications\, 2nd edition\, Walter d
 e Gruyter &amp\; Co.\, Berlin\, 2012.\nS. Puzynina and L.Q. Zamboni\, Addi
 tive properties of sets and substitutive dynamics. To appear in a forthcom
 ing book "Recent Mathematical Developments in Aperiodic Order" edited by J
 . Kellendonk\, D. Lenz and J. Savinien.\n&nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 015/12/Svetlana_Puzynina.jpg
CATEGORIES:Séminaire,Ernest
END:VEVENT
BEGIN:VTIMEZONE
TZID:Europe/Paris
X-LIC-LOCATION:Europe/Paris
BEGIN:DAYLIGHT
DTSTART:20140330T030000
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
END:DAYLIGHT
END:VTIMEZONE
END:VCALENDAR