In this paper, we investigate the factor properties and gap sequence of the Tri- bonacci sequence, the fixed point of the substitution σ（a, b, c） = （ab, ac, a）. Let Wp be the p-th occurrence of w and Gp（ω） be ...In this paper, we investigate the factor properties and gap sequence of the Tri- bonacci sequence, the fixed point of the substitution σ（a, b, c） = （ab, ac, a）. Let Wp be the p-th occurrence of w and Gp（ω） be the gap between Wp and Wp＋l. We introduce a notion of kernel for each factor w, and then give the decomposition of the factor w with respect to its kernel. Using the kernel and the decomposition, we prove the main result of this paper： for each factor w, the gap sequence {Gp（ω）}p≥1 is the Tribonacci sequence over the alphabet {G1 （ω）, G2（ω）, G4（ω）}, and the expressions of gaps are determined completely. As an application, for each factor w and p C ∈N, we determine the position of Wp. Finally we introduce a notion of spectrum for studying some typical combinatorial properties, such as power, overlap and separate of factors.展开更多
The study of the dihedral f-tilings of the sphere S2 whose prototiles are a scalene triangle and an isosceles trapezoid was initiated in a previous work. In this paper we continue this classification presenting the st...The study of the dihedral f-tilings of the sphere S2 whose prototiles are a scalene triangle and an isosceles trapezoid was initiated in a previous work. In this paper we continue this classification presenting the study of all dihedral spherical f-tilings by scalene triangles and isosceles trapezoids in some cases of adjacency.展开更多
基金supported by grants from the National Science Foundation of China(114310071127122311371210)
文摘In this paper, we investigate the factor properties and gap sequence of the Tri- bonacci sequence, the fixed point of the substitution σ（a, b, c） = （ab, ac, a）. Let Wp be the p-th occurrence of w and Gp（ω） be the gap between Wp and Wp＋l. We introduce a notion of kernel for each factor w, and then give the decomposition of the factor w with respect to its kernel. Using the kernel and the decomposition, we prove the main result of this paper： for each factor w, the gap sequence {Gp（ω）}p≥1 is the Tribonacci sequence over the alphabet {G1 （ω）, G2（ω）, G4（ω）}, and the expressions of gaps are determined completely. As an application, for each factor w and p C ∈N, we determine the position of Wp. Finally we introduce a notion of spectrum for studying some typical combinatorial properties, such as power, overlap and separate of factors.
基金Research funded by the Portuguese Government through the FCT-Fundaao para a Ciencia e a Tecnologia-under the project PEst-OE/MAT/UI4080/2011
文摘The study of the dihedral f-tilings of the sphere S2 whose prototiles are a scalene triangle and an isosceles trapezoid was initiated in a previous work. In this paper we continue this classification presenting the study of all dihedral spherical f-tilings by scalene triangles and isosceles trapezoids in some cases of adjacency.
