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start [2026/06/09 14:23] – anna.fridstart [2026/06/23 13:57] (current) – anna.frid
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 +**July 7 2026: Delaram Moradi**
 +
 +==== Past talks 2026 ====
 **June 23 2026: [[https://arxiv.org/search/math?searchtype=author&query=Cloitre,+B|Benoit Cloitre]]** //The Thue-Morse Transform// **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}}
 +
 +{{ 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.  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. 
  
-**July 7 2026: Delaram Moradi** 
  
-==== Past talks 2026 ==== 
 **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//