Relaxations of associativity and preassociativity for variadic functions
Copyright policy )Relaxations of associativity and preassociativity for variadic functions
In this paper we consider two properties of variadic functions, namely associativity and preassociativity, that are pertaining to several data and language processing tasks. We propose parameterized relaxations of these properties and provide their descriptions in terms of factorization results. We also give an example where these parameterized notions give rise to natural hierarchies of functions and indicate their potential use in measuring the degrees of associativeness and preassociativeness. We illustrate these results by several examples and constructions and discuss some open problems that lead to further directions of research.
: Computer science [C05] [Engineering, computing & technology], FOS: Computer and information sciences, Discrete Mathematics (cs.DM), 20M05, 20M32, 39B72, 68R99, Preassociativity, String function, Mathematics - Rings and Algebras, Group Theory (math.GR), : Sciences informatiques [C05] [Ingénierie, informatique & technologie], Functional equation, Axiomatization, Rings and Algebras (math.RA), Associativity, [MATH.MATH-RA] Mathematics [math]/Rings and Algebras [math.RA], FOS: Mathematics, : Mathematics [G03] [Physical, chemical, mathematical & earth Sciences], : Mathématiques [G03] [Physique, chimie, mathématiques & sciences de la terre], Variadic function, Mathematics - Group Theory, Computer Science - Discrete Mathematics
: Computer science [C05] [Engineering, computing & technology], FOS: Computer and information sciences, Discrete Mathematics (cs.DM), 20M05, 20M32, 39B72, 68R99, Preassociativity, String function, Mathematics - Rings and Algebras, Group Theory (math.GR), : Sciences informatiques [C05] [Ingénierie, informatique & technologie], Functional equation, Axiomatization, Rings and Algebras (math.RA), Associativity, [MATH.MATH-RA] Mathematics [math]/Rings and Algebras [math.RA], FOS: Mathematics, : Mathematics [G03] [Physical, chemical, mathematical & earth Sciences], : Mathématiques [G03] [Physique, chimie, mathématiques & sciences de la terre], Variadic function, Mathematics - Group Theory, Computer Science - Discrete Mathematics
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