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UID:20251121T195928EST-2186RE8utT@132.216.98.100
DTSTAMP:20251122T005928Z
DESCRIPTION:Title: $k$-abelian equivalence - an equivalence relation inbetw
 een the equality and the abelian equality.\n\nTwo words $u$ and $v$ are $k
 $-abelian equivalent if\, for each $w$ of length at most $k$\, the number 
 of occurrences of $w$ in $u$ coincides to that in $v$. The $k$-abelian equ
 ivalence is a natural equivalence relation\, in fact a congruence\, betwee
 n the equality and the abelian equality. Topics we consider in this lectur
 e are the avoidability of patterns\, the palindromicity\, and different ty
 pes of complexity issues\, in particular the number of the equivalence cla
 sses and the fluctuation of the complexity function of infinite words. We 
 show that the set of minimal elements of the equivalence classes is a rati
 onal set. Consequently\, for each parameter $k$ and alphabet size $m$\, th
 e numbers of equivalence classes of words of length $n$ form a rational se
 quence. Given $k$ and $m$ this sequence is algorithmically computable\, bu
 t in practice only on very small values of the parameters.\n\n\n	 \n\n	Semin
 ar LACIM\n		201\, av. du Président-Kennedy\, LOCAL PK-4323\, Montréal (Qc) H
 2X 3Y7\n\n\n \n
DTSTART:20170908T173000Z
DTEND:20170908T183000Z
SUMMARY:Juhani Karhumäki\, Université de Turku
URL:/mathstat/channels/event/juhani-karhumaki-universi
 te-de-turku-269971
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