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bourg, LUXEMBOURG . . . . Co-author(s): Erkko LETHONEN, Bruno TEHEUX . . . . Title of talk: Associative string functions . . . .

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Academic year: 2021

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Author: Jean-Luc MARICHAL . . . . Department: Mathematics Research Unit . . . . University: University of Luxembourg . . . . Address: 6, rue Coudenhove-Kalergi, L-1359 Luxem-

bourg, LUXEMBOURG . . . . Co-author(s): Erkko LETHONEN, Bruno TEHEUX . . . . Title of talk: Associative string functions . . . .

Abstract:

A string function over a nonempty set X is a function F : X

→ X

, where X

=

Sn≥1

X

n

. We say that such a function is associative if

F (xyz) = F (xF (y)z) , x, y, z ∈ X

,

where the tuple xyz ∈ X

is obtained by concatenating the tuples x,

y, and z. We discuss this new property and describe certain classes of

associative string functions. We also characterize the recently introduced

preassociative functions as compositions of associative string functions

with injective unary maps.

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