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題名 Characterization and Topological Behavior of Homomorphism Tree-Shifts
作者 班榮超
Ban, Jung-Chao
Chang, Chih-Hung
Hu, Wen-Guei
Lai, Guan-Yu
貢獻者 應數系
關鍵詞 Tree-SFT;Sofic tree-shift;Mixing property
日期 2021-10
上傳時間 10-Feb-2022 14:57:57 (UTC+8)
摘要 The purpose of this article is twofold. On one hand, we reveal the equivalence of shift of finite type between a one-sided shift X and its associated hom tree-shift TX, as well as the equivalence in the sofic shift. On the other hand, we investigate the interrelationship among the comparable mixing properties on tree-shifts as those on multidimensional shift spaces. They include irreducibility, topologically mixing, block gluing, and strong irreducibility, all of which are defined in the spirit of classical multidimensional shift, complete prefix code (CPC), and uniform CPC. In summary, the mixing properties defined in all three manners coincide for TX. Furthermore, an equivalence between irreducibility on TA and irreducibility on XA are seen, and so is one between topologically mixing on TA and mixing property on XA, where XA is the one-sided shift space induced by the matrix A and TA is the associated tree-shift. These equivalences are consistent with the mixing properties on X or XA when viewed as a degenerate tree-shift.
關聯 Topology and its Applications, Volume 302, 107848
資料類型 article
DOI https://doi.org/10.1016/j.topol.2021.107848
dc.contributor 應數系
dc.creator (作者) 班榮超
dc.creator (作者) Ban, Jung-Chao
dc.creator (作者) Chang, Chih-Hung
dc.creator (作者) Hu, Wen-Guei
dc.creator (作者) Lai, Guan-Yu
dc.date (日期) 2021-10
dc.date.accessioned 10-Feb-2022 14:57:57 (UTC+8)-
dc.date.available 10-Feb-2022 14:57:57 (UTC+8)-
dc.date.issued (上傳時間) 10-Feb-2022 14:57:57 (UTC+8)-
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/139040-
dc.description.abstract (摘要) The purpose of this article is twofold. On one hand, we reveal the equivalence of shift of finite type between a one-sided shift X and its associated hom tree-shift TX, as well as the equivalence in the sofic shift. On the other hand, we investigate the interrelationship among the comparable mixing properties on tree-shifts as those on multidimensional shift spaces. They include irreducibility, topologically mixing, block gluing, and strong irreducibility, all of which are defined in the spirit of classical multidimensional shift, complete prefix code (CPC), and uniform CPC. In summary, the mixing properties defined in all three manners coincide for TX. Furthermore, an equivalence between irreducibility on TA and irreducibility on XA are seen, and so is one between topologically mixing on TA and mixing property on XA, where XA is the one-sided shift space induced by the matrix A and TA is the associated tree-shift. These equivalences are consistent with the mixing properties on X or XA when viewed as a degenerate tree-shift.
dc.format.extent 560987 bytes-
dc.format.mimetype application/pdf-
dc.relation (關聯) Topology and its Applications, Volume 302, 107848
dc.subject (關鍵詞) Tree-SFT;Sofic tree-shift;Mixing property
dc.title (題名) Characterization and Topological Behavior of Homomorphism Tree-Shifts
dc.type (資料類型) article
dc.identifier.doi (DOI) 10.1016/j.topol.2021.107848
dc.doi.uri (DOI) https://doi.org/10.1016/j.topol.2021.107848