Permutations and negative beta-shifts
Emilie Charlier, Wolfgang Steiner (IRIF)
TL;DR
This paper extends Elizalde's 2011 characterization of permutations generated by positive beta-transformations to the case of negative bases, providing a comprehensive understanding of permutation patterns in negative beta-shifts.
Contribution
It offers a new characterization of permutations arising from negative beta-transformations, complementing previous work on positive bases.
Findings
Established a characterization of permutations from negative beta-shifts.
Extended the theory of beta-transformations to negative bases.
Provided insights into the structure of permutations in negative beta-shifts.
Abstract
Elizalde (2011) characterized which permutations can be obtained by ordering consecutive elements in the trajectories of (positive) beta-transformations and beta-shifts. We prove similar results for negative bases beta.
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Taxonomy
Topicssemigroups and automata theory · Advanced Algebra and Logic · graph theory and CDMA systems