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start [2026/04/29 09:57] – anna.fridstart [2026/06/24 12:59] (current) – anna.frid
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 ==== Upcoming talks ====  ==== Upcoming talks ==== 
  
-**May 12 2026: Léo Vivion**+To be scheduled later 
 + 
 +<del>**July 7 2026: Delaram Moradi**</del> 
 + 
 +==== Past talks 2026 ==== 
 +**June 23 2026: [[https://arxiv.org/search/math?searchtype=author&query=Cloitre,+B|Benoit Cloitre]]** //The Thue-Morse Transform// 
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 +{{ seminar2026:20260623cloitre.pdf |slides}} 
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 +{{ seminar2026:20260623cloitre.mp4 |video of the talk}} 
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 +We define a transform $T$ on binary words. Given a binary word, we use the positions of its zeros and ones to build a new binary word. Applied to the alternating word $a_0 = 0101\ldots$, the transform gives the Thue-Morse word. We then study the orbit $a_m = T^m(a_0)$, together with the sequences $u_m$ and $v_m$ giving the positions of the ones and the zeros in $a_m$. We obtain an explicit formula for $a_m(n)$ in terms of the binary digits of $n$ and $m-1$. From this formula we derive Prouhet-Tarry-Escott identities, composition formulas that generalize the identities for evil and odious numbers, and a recurrence formula for the factor complexity of $a_m$. We end with a few directions, such as applying the transform to the Fibonacci word, which yields the Fibonacci-Thue-Morse word. 
  
-**May 26 2026: Reem Yassawi** 
  
 **June 9 2026:  [[https://kmlinux.fjfi.cvut.cz/~balkolub/| Ľubomíra Dvořáková]]** //Attractors of sequences coding beta-integers// **June 9 2026:  [[https://kmlinux.fjfi.cvut.cz/~balkolub/| Ľubomíra Dvořáková]]** //Attractors of sequences coding beta-integers//
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 +{{ seminar2026:20260609dvorakova.pdf |slides}}
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 +{{ seminar2026:20260609dvorakova.mp4 |video of the talk}}
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 String attractor is an intensively studied object in Combinatorics on Words. String attractor is an intensively studied object in Combinatorics on Words.
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 Simple Parry sequences have been recently studied from this point of view and (not necessarily minimal) attractors of their prefixes have been described and a conjecture that attractors of alphabet size should be sufficient was stated. We prove this conjecture. Moreover, we provide attractors of prefixes of some particular form of binary non-simple Parry sequences. Simple Parry sequences have been recently studied from this point of view and (not necessarily minimal) attractors of their prefixes have been described and a conjecture that attractors of alphabet size should be sufficient was stated. We prove this conjecture. Moreover, we provide attractors of prefixes of some particular form of binary non-simple Parry sequences.
  
-**June 23 2026: Benoit Clôitre** 
  
-**July 7 2026: Delaram Moradi**+**May 12 2026: [[https://www-lmpa.univ-littoral.fr/~lvivion/|Léo Vivion]]** //New examples of words for which binomial complexities and subword complexity coincide// 
 + 
 +{{ seminar2026:20260512vivion.pdf |slides}} 
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 +(The talk was not recorded at the speaker's request.) 
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 +In 2015, Rigo and Salimov introduced a family of complexities that forms a scale between abelian complexity and factor complexity: the $k$-binomial complexities. In particular, they showed that Sturmian words satisfy the following remarkable combinatorial property: their $2$-binomial complexity is equal to their factor complexity. Since then, the only other known example satisfying this property is the Tribonacci word. 
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 +In this talk, I will present some stability results for words whose $k$-binomial complexities coincide with their factor complexity, notably under letter deletion and a coloring operation. These stability properties allow to show that several well-known families of words also have their $2$-binomial complexity equal to their factor complexity.
  
-==== Past talks 2026 ==== 
  
 **April 28 2026:  [[https://sites.google.com/ug.uchile.cl/espinoza|Bastiàn Espinoza]]** //The Thue-Morse word in base 3/2// **April 28 2026:  [[https://sites.google.com/ug.uchile.cl/espinoza|Bastiàn Espinoza]]** //The Thue-Morse word in base 3/2//