The Genetic Codes: Mathematical Formulae and an Inverse Symmetry-Information Relationship

First, mathematical formulae faithfully describing the distributions of amino acids and codons and reproducing the degeneracies in the various known genetic codes, including the standard genetic code, are constructed, by hand. Second, we summarize another mathematical approach relying on the use of q-deformations to describe these same genetic codes, and add a new application not considered before. Third, by considering these same genetic codes, we find, qualitatively, that an inverse symmetry-information relationship exists.