Displaying similar documents to “On automatic infinite permutations∗”

On automatic infinite permutations

Anna Frid, Luca Zamboni (2012)

RAIRO - Theoretical Informatics and Applications

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An infinite permutation is a linear ordering of N. We study properties of infinite permutations analogous to those of infinite words, and show some resemblances and some differences between permutations and words. In this paper, we try to extend to permutations the notion of automaticity. As we shall show, the standard definitions which are equivalent in the case of words are not equivalent in the context of permutations. We investigate...

On automatic infinite permutations

Anna Frid, Luca Zamboni (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Similarity:

An infinite permutation is a linear ordering of N. We study properties of infinite permutations analogous to those of infinite words, and show some resemblances and some differences between permutations and words. In this paper, we try to extend to permutations the notion of automaticity. As we shall show, the standard definitions which are equivalent in the case of words are not equivalent in the context of permutations. We investigate the relationships between these definitions and...

Words over an ordered alphabet and suffix permutations

Jean-Pierre Duval, Arnaud Lefebvre (2002)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Given an ordered alphabet and a permutation, according to the lexicographic order, on the set of suffixes of a word w , we present in this article a linear time and space method to determine whether a word w ' has the same permutation on its suffixes. Using this method, we are then also able to build the class of all the words having the same permutation on their suffixes, first of all the smallest one. Finally, we note that this work can lead to a method for generating a Lyndon word randomly...

Axial permutations of ω²

Paweł Klinga (2016)

Colloquium Mathematicae

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We prove that every permutation of ω² is a composition of a finite number of axial permutations, where each axial permutation moves only a finite number of elements on each axis.

Growth rates for subclasses of Av(321).

Albert, M.H., Atkinson, M.D., Brignall, R., Ruškuc, N., Smith, Rebecca, West, J. (2010)

The Electronic Journal of Combinatorics [electronic only]

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Some new facts about group 𝒢 generated by the family of convergent permutations

Roman Wituła, Edyta Hetmaniok, Damian Słota (2017)

Open Mathematics

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The aim of this paper is to present some new and essential facts about group 𝒢 generated by the family of convergent permutations, i.e. the permutations on ℕ preserving the convergence of series of real terms. We prove that there exist permutations preserving the sum of series which do not belong to 𝒢. Additionally, we show that there exists a family G (possessing the cardinality equal to continuum) of groups of permutations on ℕ such that each one of these groups is different than...