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$N$ -ary hyperstructures associated to the genotypes of $F_{2}$ -offspring

M. Al-Tahan

Department of Mathematics, Lebanese International University, Bekaa, Lebanon

E-mail Address: madeline.tahan@liu.edu.lb

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and

B. Davvaz

Department of Mathematics, Yazd University, Yazd, Iran

E-mail Address: davvaz@yazd.ac.ir

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https://doi.org/10.1142/S1793524517501182Cited by:4 (Source: Crossref)

Abstract

In this paper, we consider an application of hyperstructure theory in biological inheritance in which we deal with $n$ -ary hyperstructures associated to the genotypes of the second generation $F_{2}$ for $n = 2, 3, 4$ . First, we define a hyperoperation × (mating) on $F_{2}$ and prove that it is a cyclic $H_{v}$ -semigroup under the defined hyperoperation. Then we define a ternary hyperstructure $f$ associated to the genotypes of $F_{2}$ and prove that $(F_{2}, f)$ is a ternary $H_{v}$ -semigroup. Finally, we define a $4$ -ary hyperstructure $g$ associated to the genotypes of $F_{2}$ and prove that $(F_{2}, g)$ is a $4$ -ary $H_{v}$ -semigroup.

Keywords:

AMSC: 92D10, 20N20

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