scholarly journals Continued fraction algorithm for Sturmian colorings of trees

2017 ◽  
Vol 39 (9) ◽  
pp. 2541-2569
Author(s):  
DONG HAN KIM ◽  
SEONHEE LIM
Keyword(s):  
Continued Fraction ◽  
Vertex Coloring ◽  
Regular Tree ◽  
Sturmian Words ◽  
Number Of Classes ◽  
Fraction Algorithm

Factor complexity $b_{n}(\unicode[STIX]{x1D719})$ for a vertex coloring $\unicode[STIX]{x1D719}$ of a regular tree is the number of classes of $n$-balls up to color-preserving automorphisms. Sturmian colorings are colorings of minimal unbounded factor complexity $b_{n}(\unicode[STIX]{x1D719})=n+2$. In this article, we prove an induction algorithm for Sturmian colorings using colored balls in a way analogous to the continued fraction algorithm for Sturmian words. Furthermore, we characterize Sturmian colorings in terms of the data appearing in the induction algorithm.

scholarly journals A continued fraction algorithm for real algebraic numbers

1972 ◽  
Vol 26 (119) ◽  
pp. 785-785 ◽  
Author(s):  
David G. Cantor ◽  
Paul H. Galyean ◽  
Horst G. Zimmer
Keyword(s):  
Continued Fraction ◽  
Algebraic Numbers ◽  
Fraction Algorithm

scholarly journals Complex Method on Octagonal Number

2020 ◽  
Vol 8 (4S5) ◽  
pp. 11-13
Keyword(s):  
Number Theory ◽  
Continued Fraction ◽  
Complex Method ◽  
Polygonal Numbers ◽  
Fraction Algorithm

In Number theory Study of polygonal numbers is rich in varity. In this paper we establish a Complex Octagonal Number using Continued Fraction algorithm.

A NEW SYMMETRIC TWO-DIMENSIONAL ALGORITHM

2006 ◽  
Vol 02 (04) ◽  
pp. 489-498
Author(s):  
PEDRO FORTUNY AYUSO ◽  
FRITZ SCHWEIGER
Keyword(s):  
Continued Fractions ◽  
Continued Fraction ◽  
Dual Graph ◽  
Plane Curve ◽  
Singularity Theory ◽  
Main Topic ◽  
Two Dimensional ◽  
Dimension 2 ◽  
Multidimensional Continued Fraction ◽  
Fraction Algorithm

Continued fractions are deeply related to Singularity Theory, as the computation of the Puiseux exponents of a plane curve from its dual graph clearly shows. Another closely related topic is Euclid's Algorithm for computing the gcd of two integers (see [2] for a detailed overview). In the first section, we describe a subtractive algorithm for computing the gcd of n integers, related to singularities of curves in affine n-space. This gives rise to a multidimensional continued fraction algorithm whose version in dimension 2 is the main topic of the paper.

scholarly journals The length of the continued fraction expansion for a class of rational functions in

1991 ◽  
Vol 34 (1) ◽  
pp. 7-17 ◽  
Author(s):  
Arnold Knopfmacher
Keyword(s):  
Finite Field ◽  
Continued Fraction ◽  
Rational Functions ◽  
Euclidean Algorithm ◽  
Continued Fraction Expansion ◽  
Partial Quotients ◽  
Fraction Algorithm

A study is made of the length L(h, k) of the continued fraction algorithm for h/k where h and k are co-prime polynomials in a finite field. In addition we investigate the sum of the degrees of the partial quotients in this expansion for h/k, h, k in . The above continued fraction is determined by means of the Euclidean algorithm for the polynomials h, k in .

A continued fraction algorithm

1981 ◽  
Vol 37 (1) ◽  
pp. 149-156 ◽  
Author(s):  
P. Van der Cruyssen
Keyword(s):  
Continued Fraction ◽  
Fraction Algorithm

A continued fraction algorithm

1967 ◽  
Vol 7 (1) ◽  
pp. 76-80
Author(s):  
Hans Riesel
Keyword(s):  
Continued Fraction ◽  
Fraction Algorithm

A hybrid fast Hankel transform algorithm for electromagnetic modeling

Geophysics ◽  
1989 ◽  
Vol 54 (2) ◽  
pp. 263-266 ◽  
Author(s):  
Walter L. Anderson
Keyword(s):  
Continued Fraction ◽  
Good Accuracy ◽  
Hybrid Approach ◽  
Hankel Transform ◽  
Kernel Functions ◽  
Electromagnetic Modeling ◽  
Electromagnetic Problems ◽  
Special Cases ◽  
Standard Fortran ◽  
Fraction Algorithm

A hybrid fast Hankel transform algorithm has been developed that uses several complementary features of two existing algorithms: Anderson’s digital filtering or fast Hankel transform (FHT) algorithm and Chave’s quadrature and continued fraction algorithm. A hybrid FHT subprogram (called HYBFHT) written in standard Fortran-77 provides a simple user interface to call either subalgorithm. The hybrid approach is an attempt to combine the best features of the two subalgorithms in order to minimize the user’s coding requirements and to provide fast execution and good accuracy for a large class of electromagnetic problems involving various related Hankel transform sets with multiple arguments. Special cases of Hankel transforms of double‐order and double‐argument are discussed, where use of HYBFHT is shown to be advantageous for oscillatory kernel functions.

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