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UID:20250724T073810EDT-3165RusavU@132.216.98.100
DTSTAMP:20250724T113810Z
DESCRIPTION:On a conjecture about regularity and $\ell$-abelian complexity.
 \n\nSince the fundamental work of Cobham\, the so-called automatic sequenc
 es have been extensively studied. A natural generalization of automatic se
 quences over an infinite alphabet is given by the notion of $k$-regular se
 quences\, introduced by Allouche and Shallit in 1992. The $k$-regularity o
 f a sequence provides us with structural information about how the differe
 nt terms are related to each other. We show that a sequence satisfying a c
 ertain symmetry property is 2-regular. We apply this theorem to develop a 
 general approach for studying the ℓ-abelian complexity of 2-automatic sequ
 ences. In particular\, we prove that the period-doubling word and the Thue
 –Morse word have 2-abelian complexity sequences that are 2-regular. Along 
 the way\, we also prove that the 2-block codings of these two words have 1
 -abelian complexity sequences that are 2-regular. The computation and argu
 ments leading to these results fit into a quite general scheme that we hop
 e can be used again to prove additional regularity results.\n
DTSTART:20170310T183000Z
DTEND:20170310T193000Z
LOCATION:Room PK-4323\, CA\, Pavillon Président-Kennedy
SUMMARY:Élise Vandomme\, Université du Québec à Montréal
URL:/mathstat/channels/event/elise-vandomme-universite
 -du-quebec-montreal-266724
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