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RESEARCH PRODUCT

On generalized Lyndon words

Antonio RestivoChristophe ReutenauerFrancesco Dolce

subject

FOS: Computer and information sciencesGeneral Computer ScienceDiscrete Mathematics (cs.DM)Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)68R15Characterization (mathematics)Lexicographical orderTheoretical Computer ScienceLyndon wordsCombinatoricsFactorizationPosition (vector)Free monoidFOS: MathematicsOrder (group theory)Mathematics - CombinatoricsCombinatorics (math.CO)Word (group theory)Computer Science::Formal Languages and Automata TheoryMathematicsComputer Science - Discrete Mathematics

description

Abstract A generalized lexicographical order on infinite words is defined by choosing for each position a total order on the alphabet. This allows to define generalized Lyndon words. Every word in the free monoid can be factorized in a unique way as a nonincreasing factorization of generalized Lyndon words. We give new characterizations of the first and the last factor in this factorization as well as new characterization of generalized Lyndon words. We also give more specific results on two special cases: the classical one and the one arising from the alternating lexicographical order.

yearjournalcountryeditionlanguage
2018-12-11
http://arxiv.org/abs/1812.04515