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shorttalksmarch2021 [2022/10/30 23:01] – old revision restored (2021/03/16 20:31) 139.124.146.3shorttalksmarch2021 [2022/10/30 23:01] (current) – old revision restored (2021/01/26 19:13) 139.124.146.3
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 ==== Speakers ==== ==== Speakers ====
  
-**15:00 Jane D. Palacio** //Coverable bi-infinite substitution shifts//+** Ibai Aedo ** //On long arithmetic progressions in binary Morse-like words// 
 + 
 +In this talk, I will present a joint work with Uwe Grimm, Yasushi Nagai and Petra Staynova based on a recent preprint: arXiv:2101.02056. Regarding the Prouhet-Thue-Morse word as a two-colouring of the positive integers, we look for long monochromatic arithmetic progressions occurring in the sequence. 
 + 
 +The size of the longest arithmetic progression of difference $d=2^n-1$ was previously established by O. Parshina. Using a different approach, mainly based on exploiting the substitution structure of the Prouhet-Thue-Morse word, we will show how we can re-establish this result and find another series of long arithmetic progressions of difference d=2^n+1. Then, we will comment on a generalisation of these results for a special class of bijective binary words, and we will finish with some more general results and some open questions. 
 + 
 +**Francesco Dolce** //On morphisms preserving palindromic richness// 
 + 
 +A finite word is said to be rich if it has maximal number of palindromic factors (this is known to be the length of the word plus one). This definition can be naturally extended to infinite words.Sturmian words and Rote complementary symmetric sequences form two classes of binary rich words, while strict episturmian words and words coding symmetric interval exchange transformations give us other examples on larger alphabets. 
 +In this talk we study homomorphisms of the free monoid which allow to construct new rich words from already known rich words. In particular, we focus on two types of morphisms: Arnoux-Rauzy morphisms and morphisms from Class $P_{ret}$. These morphisms contain Sturmian morphisms as a subclass. We show that Arnoux-Rauzy morphisms preserve the set of all rich words. 
 +We also characterize $P_{ret}$ morphisms which preserve richness on binary alphabet. 
 +This is a joint work with Edita Pelantová. 
 + 
 +**Anna E. Frid** //The semigroup of trimmed morphisms// 
 + 
 +We start a study of possible orders of morphic images of words. In the binary case, it is known that every morphism is either order-preserving or order-reversing. For larger alphabets, the situation can be much more complicated.  
 + 
 +**Jane D. Palacio** //Coverable bi-infinite substitution shifts//
  
 A finite or infinite word $w$ is said to be coverable if it can be formed by A finite or infinite word $w$ is said to be coverable if it can be formed by
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 This is joint work with Manuel Joseph Loquias and Eden Delight Miro. This is joint work with Manuel Joseph Loquias and Eden Delight Miro.
  
-**15:30 Ibai Aedo ** //On long arithmetic progressions in binary Morse-like words// 
  
-In this talk, I will present a joint work with Uwe Grimm, Yasushi Nagai and Petra Staynova based on a recent preprint: arXiv:2101.02056. Regarding the Prouhet-Thue-Morse word as a two-colouring of the positive integers, we look for long monochromatic arithmetic progressions occurring in the sequence. +** Jeffrey  Shallit** //Robbins and Ardila meet Berstel//
- +
-The size of the longest arithmetic progression of difference $d=2^n-1$ was previously established by O. Parshina. Using a different approach, mainly based on exploiting the substitution structure of the Prouhet-Thue-Morse word, we will show how we can re-establish this result and find another series of long arithmetic progressions of difference d=2^n+1. Then, we will comment on a generalisation of these results for a special class of bijective binary words, and we will finish with some more general results and some open questions. +
- +
-**16:00 Francesco Dolce** //On morphisms preserving palindromic richness// +
- +
-A finite word is said to be rich if it has maximal number of palindromic factors (this is known to be the length of the word plus one). This definition can be naturally extended to infinite words.Sturmian words and Rote complementary symmetric sequences form two classes of binary rich words, while strict episturmian words and words coding symmetric interval exchange transformations give us other examples on larger alphabets. +
-In this talk we study homomorphisms of the free monoid which allow to construct new rich words from already known rich words. In particular, we focus on two types of morphisms: Arnoux-Rauzy morphisms and morphisms from Class $P_{ret}$. These morphisms contain Sturmian morphisms as a subclass. We show that Arnoux-Rauzy morphisms preserve the set of all rich words. +
-We also characterize $P_{ret}$ morphisms which preserve richness on binary alphabet. +
-This is a joint work with Edita Pelantová. +
- +
-**16:30 Jeffrey  Shallit** //Robbins and Ardila meet Berstel//+
  
 In this short talk I show how to obtain a result of Robbins and (later) In this short talk I show how to obtain a result of Robbins and (later)
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 that once you have Berstel's transducer, the rest follows by purely that once you have Berstel's transducer, the rest follows by purely
 computational means. computational means.
- 
- 
-**17:00 Anna E. Frid** //The semigroup of trimmed morphisms// 
- 
-We start a study of possible orders of morphic images of words. In the binary case, it is known that every morphism is either order-preserving or order-reversing. For larger alphabets, the situation can be much more complicated.  
-