String attractors of Rote sequences
In this paper, we describe minimal string attractors (of size two) of pseudopalindromic prefixes of standard complementary-symmetric Rote sequences. Such a class of Rote sequences forms a subclass of binary generalized pseudostandard sequences, i.e., of sequences obtained when iterating palindromic...
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Discrete Mathematics & Theoretical Computer Science
2024-11-01
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| author | Lubomíra Dvořáková Veronika Hendrychová |
| author_facet | Lubomíra Dvořáková Veronika Hendrychová |
| author_sort | Lubomíra Dvořáková |
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| description | In this paper, we describe minimal string attractors (of size two) of pseudopalindromic prefixes of standard complementary-symmetric Rote sequences. Such a class of Rote sequences forms a subclass of binary generalized pseudostandard sequences, i.e., of sequences obtained when iterating palindromic and antipalindromic closures. When iterating only palindromic closure, palindromic prefixes of standard Sturmian sequences are obtained and their string attractors are of size two. However, already when iterating only antipalindromic closure, antipalindromic prefixes of binary pseudostandard sequences are obtained and we prove that the minimal string attractors are of size three in this case. We conjecture that the pseudopalindromic prefixes of any binary generalized pseudostandard sequence have a minimal string attractor of size at most four. |
| format | Article |
| id | doaj-art-e3f28c3bc4a5409e87a8b53b45ebcbe7 |
| institution | OA Journals |
| issn | 1365-8050 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj-art-e3f28c3bc4a5409e87a8b53b45ebcbe72025-08-20T01:49:33ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502024-11-01vol. 26:3Combinatorics10.46298/dmtcs.1238512385String attractors of Rote sequencesLubomíra DvořákováVeronika HendrychováIn this paper, we describe minimal string attractors (of size two) of pseudopalindromic prefixes of standard complementary-symmetric Rote sequences. Such a class of Rote sequences forms a subclass of binary generalized pseudostandard sequences, i.e., of sequences obtained when iterating palindromic and antipalindromic closures. When iterating only palindromic closure, palindromic prefixes of standard Sturmian sequences are obtained and their string attractors are of size two. However, already when iterating only antipalindromic closure, antipalindromic prefixes of binary pseudostandard sequences are obtained and we prove that the minimal string attractors are of size three in this case. We conjecture that the pseudopalindromic prefixes of any binary generalized pseudostandard sequence have a minimal string attractor of size at most four.http://dmtcs.episciences.org/12385/pdfmathematics - combinatorics68r15 |
| spellingShingle | Lubomíra Dvořáková Veronika Hendrychová String attractors of Rote sequences Discrete Mathematics & Theoretical Computer Science mathematics - combinatorics 68r15 |
| title | String attractors of Rote sequences |
| title_full | String attractors of Rote sequences |
| title_fullStr | String attractors of Rote sequences |
| title_full_unstemmed | String attractors of Rote sequences |
| title_short | String attractors of Rote sequences |
| title_sort | string attractors of rote sequences |
| topic | mathematics - combinatorics 68r15 |
| url | http://dmtcs.episciences.org/12385/pdf |
| work_keys_str_mv | AT lubomiradvorakova stringattractorsofrotesequences AT veronikahendrychova stringattractorsofrotesequences |