Jordan algebras arising from intermolecular recombination

ABSTRACT

We use computer algebra to show that a linearization of the operation of intermolecular recombination from theoretical genetics satisfies a nonassociative polynomial identity of degree 4 which implies the Jordan identity. We use the representation theory of the symmetric group to decompose this new identity into its irreducible components. We show that this new identity implies all the identities of degree ≤ 6 satisfied by intermolecular recombination.

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.3 Numerical Linear Algebra

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computations on polynomials

  J. Computer Applications
  J.3 LIFE AND MEDICAL SCIENCES
      Subjects: Biology and genetics

General Terms:
Algorithms, Theory