Associative string functions

Erkko Lehtonen; Jean Luc Marichal; Bruno Teheux

doi:10.1142/S1793557114500594

Associative string functions

Erkko Lehtonen, Jean Luc Marichal, Bruno Teheux

Mathematics

University of Luxembourg

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We introduce the concept of associativity for string functions, where a string function is a unary operation on the set of strings over a given alphabet. 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. Finally, we provide descriptions of the classes of associative and preassociative functions which depend only on the length of the input.

Original language	British English
Article number	1450059
Journal	Asian-European Journal of Mathematics
Volume	7
Issue number	4
DOIs	https://doi.org/10.1142/S1793557114500594
State	Published - 23 Dec 2014

Keywords

Associativity
axiomatization
functional equation
preassociativity
string function

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10.1142/S1793557114500594

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title = "Associative string functions",

abstract = "We introduce the concept of associativity for string functions, where a string function is a unary operation on the set of strings over a given alphabet. 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. Finally, we provide descriptions of the classes of associative and preassociative functions which depend only on the length of the input.",

keywords = "Associativity, axiomatization, functional equation, preassociativity, string function",

author = "Erkko Lehtonen and Marichal, {Jean Luc} and Bruno Teheux",

note = "Funding Information: This work was developed within the FCT Project PEst-OE/MAT/UI0143/2014 of CAUL, FCUL. It is also supported by the internal research project F1R-MTH-PUL-12RDO2 of the University of Luxembourg. The authors would like to thank the anonymous reviewer for timely and helpful suggestions. Publisher Copyright: {\textcopyright} 2014 World Scientific Publishing Company.",

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AU - Marichal, Jean Luc

AU - Teheux, Bruno

N1 - Funding Information: This work was developed within the FCT Project PEst-OE/MAT/UI0143/2014 of CAUL, FCUL. It is also supported by the internal research project F1R-MTH-PUL-12RDO2 of the University of Luxembourg. The authors would like to thank the anonymous reviewer for timely and helpful suggestions. Publisher Copyright: © 2014 World Scientific Publishing Company.

PY - 2014/12/23

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N2 - We introduce the concept of associativity for string functions, where a string function is a unary operation on the set of strings over a given alphabet. 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. Finally, we provide descriptions of the classes of associative and preassociative functions which depend only on the length of the input.

AB - We introduce the concept of associativity for string functions, where a string function is a unary operation on the set of strings over a given alphabet. 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. Finally, we provide descriptions of the classes of associative and preassociative functions which depend only on the length of the input.

KW - Associativity

KW - axiomatization

KW - functional equation

KW - preassociativity

KW - string function

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JO - Asian-European Journal of Mathematics

JF - Asian-European Journal of Mathematics

IS - 4

M1 - 1450059

ER -

Associative string functions

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Keywords

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