Algebraic hyperstructures associated to biological inheritance

After introducing the notion of hyperstructures about 80 years ago, a number of researches on its applications have been done. This paper can be considered as one of its applications on Biology. It is well known that biological inheritance is related to Mathematics in the sense of probability. In this paper, we consider another relationship between inheritance and Mathematics in which we present a connection between it and hyperstructures. First, we present examples of five different types of Non- Mendelian inheritance and study, for the first time, their relation with hyperstucture theory. Then we make some hypothetical crosses for the n- hybrid case for both simple and incomplete inheritances and study their relations with hyperstructures.