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]
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Abstract
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.
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khoshnoudirad2016journalerratum
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| Authors | ;Daniel Khoshnoudirad |
| Journal | Plant disease |
| Year | 2016 |
| DOI |
10.13069/jacodesmath.00924
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