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## Erratum to “A further study for the upper bound of the cardinality of Farey vertices and applications in discrete geometry” [J. Algebra Comb. Discrete Appl. 2(3) (2015) 169-190]

The equation (4) on the page 178 of the paper previously published has to be corrected. We had only handled the case of the Farey vertices for which $\min\left(\left\lfloor\dfrac{2m}{sr'}\right\rfloor,\left\lfloor\dfrac{n}{s'r}\right\rfloor \right)\in\mathbb{N}^{*}$. In fact we had to distinguish two cases: $\min\left(\left\lfloor\dfrac{2m}{sr'}\right\rfloor,\left\lfloor\dfrac{n}{s'r}\right\rfloor \right)\in\mathbb{N}^{*}$ and $\min\left(\left\lfloor\dfrac{2m}{sr'}\right\rfloor,\left\lfloor\dfrac{n}{s'r}\right\rfloor \right)=0$. However, we highlight the correct results of the original paper and its applications. We underline that in this work, we still brought several contributions. These contributions are: applying the fundamental formulas of Graph Theory to the Farey diagram of order $(m,n)$, finding a good upper bound for the degree of a Farey vertex and the relations between the Farey diagrams and the linear diophantine equations.
Combinatorial number theory, Farey diagrams, Theoretical computer sciences, Discrete planes, Diophantine equations, Arithmetical geometry, Combinatorial geometry, Discrete geometry, Graph theory in computer sciences
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Subjects Engineering Articles Author: Daniel Khoshnoudirad Publication Date : May 15, 2016
 Bibtex @correction { jacodesmath285455, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2016}, volume = {3}, pages = {105 - 123}, doi = {10.13069/jacodesmath.00924}, title = {Erratum to “A further study for the upper bound of the cardinality of Farey vertices and applications in discrete geometry” [J. Algebra Comb. Discrete Appl. 2(3) (2015) 169-190]}, key = {cite}, author = {Khoshnoudirad, Daniel} } APA Khoshnoudirad, D . (2016). Erratum to “A further study for the upper bound of the cardinality of Farey vertices and applications in discrete geometry” [J. Algebra Comb. Discrete Appl. 2(3) (2015) 169-190] . Journal of Algebra Combinatorics Discrete Structures and Applications , 3 (2) , 105-123 . DOI: 10.13069/jacodesmath.00924 MLA Khoshnoudirad, D . "Erratum to “A further study for the upper bound of the cardinality of Farey vertices and applications in discrete geometry” [J. Algebra Comb. Discrete Appl. 2(3) (2015) 169-190]" . Journal of Algebra Combinatorics Discrete Structures and Applications 3 (2016 ): 105-123 Chicago Khoshnoudirad, D . "Erratum to “A further study for the upper bound of the cardinality of Farey vertices and applications in discrete geometry” [J. Algebra Comb. Discrete Appl. 2(3) (2015) 169-190]". Journal of Algebra Combinatorics Discrete Structures and Applications 3 (2016 ): 105-123 RIS TY - JOUR T1 - Erratum to “A further study for the upper bound of the cardinality of Farey vertices and applications in discrete geometry” [J. Algebra Comb. Discrete Appl. 2(3) (2015) 169-190] AU - Daniel Khoshnoudirad Y1 - 2016 PY - 2016 N1 - doi: 10.13069/jacodesmath.00924 DO - 10.13069/jacodesmath.00924 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 105 EP - 123 VL - 3 IS - 2 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.00924 UR - https://doi.org/10.13069/jacodesmath.00924 Y2 - 2020 ER - EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications Erratum to “A further study for the upper bound of the cardinality of Farey vertices and applications in discrete geometry” [J. Algebra Comb. Discrete Appl. 2(3) (2015) 169-190] %A Daniel Khoshnoudirad %T Erratum to “A further study for the upper bound of the cardinality of Farey vertices and applications in discrete geometry” [J. Algebra Comb. Discrete Appl. 2(3) (2015) 169-190] %D 2016 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 3 %N 2 %R doi: 10.13069/jacodesmath.00924 %U 10.13069/jacodesmath.00924 ISNAD Khoshnoudirad, Daniel . "Erratum to “A further study for the upper bound of the cardinality of Farey vertices and applications in discrete geometry” [J. Algebra Comb. Discrete Appl. 2(3) (2015) 169-190]". Journal of Algebra Combinatorics Discrete Structures and Applications 3 / 2 (May 2016): 105-123 . https://doi.org/10.13069/jacodesmath.00924 AMA Khoshnoudirad D . Erratum to “A further study for the upper bound of the cardinality of Farey vertices and applications in discrete geometry” [J. Algebra Comb. Discrete Appl. 2(3) (2015) 169-190]. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016; 3(2): 105-123. Vancouver Khoshnoudirad D . Erratum to “A further study for the upper bound of the cardinality of Farey vertices and applications in discrete geometry” [J. Algebra Comb. Discrete Appl. 2(3) (2015) 169-190]. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016; 3(2): 105-123.

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