Polynomial identities for ternary intermolecular recombination

Murray Bremner
2010 Discrete and Continuous Dynamical Systems. Series S  
The operation of binary intermolecular recombination, originating in the theory of DNA computing, permits a natural generalization to n-ary operations which perform simultaneous recombination of n molecules. In the case n = 3, we use computer algebra to determine the polynomial identities of degree ≤ 9 satisfied by this trilinear nonassociative operation. Our approach requires computing a basis for the nullspace of a large integer matrix, and for this we compare two methods: (i) the row
more » ... (i) the row canonical form, and (ii) the Hermite normal form with lattice basis reduction. In the conclusion, we formulate some conjectures for the general case of n-ary intermolecular recombination.
doi:10.3934/dcdss.2011.4.1387 fatcat:2itmjzgvq5gk7myxfywfu5pzzy