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In this book, we find a Markov basis B and toric ideals for (n^2-3n)/3ž3žn/3 - contingency tables with fixed two dimensional marginals, n is a multiple of 3 greater than or equal 6, also we give a new model of permutation the pieces of nucleotides in aligned DNA sequences. Then we used the action of the largest subgroup H of dihedral group D_n on these contingency tables and B to find six types of (n^2-3n)/3ž3žn/3 - contingency tables with fixed two dimensional marginal, such that the Markov basis B for (n^2-3n)/3ž3žn/3 - contingency tables is H invariant, from these types a new model of genetic algorithm of permutation of the pieces of Nucleotides in aligned DNA sequences is given.

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Prof. Husein Hadi Abbass is the Dean Assistant post for Scientific Affairs in the Faculty of Computer Science and Mathematics, university of Kufa - Iraq. He obtained master´s degree in applied mathematics from the Technology University in Iraq in 1995. He has publications in Algebra, MV-algebra, Image Processing, Algebraic Statistics, Fuzzy maths.

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