Existence of words over a binary alphabet free from squares with mismatches
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Nikita V. Kotlyarov
Abstract
The paper is concerned with the problem of existence of periodic structures in words from formal languages. Squares (that is, fragments of the form xx, where x is an arbitrary word) and Δ-squares (that is, fragments of the form xy, where a word x differs from a word y by at most Δ letters) are considered as periodic structures. We show that in a binary alphabet there exist arbitrarily long words free from Δ-squares with length at most 4Δ+4. In particular, a method of construction of such words for any Δ is given.
Originally published in Diskretnaya Matematika (2018) 30, №2, 37–54 (in Russian).
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Convergence to the local time of Brownian meander
- Cardinality of generating sets for operations from the Post lattice classes
- Existence of words over a binary alphabet free from squares with mismatches
- Centrally essential rings
- Improved asymptotic estimates for the numbers of correlation-immune and k-resilient vectorial Boolean functions
Articles in the same Issue
- Frontmatter
- Convergence to the local time of Brownian meander
- Cardinality of generating sets for operations from the Post lattice classes
- Existence of words over a binary alphabet free from squares with mismatches
- Centrally essential rings
- Improved asymptotic estimates for the numbers of correlation-immune and k-resilient vectorial Boolean functions
