Molecularly Accessible Permutations
The propagation of text expressed in an n-letter alphabet, An, may be effected by any of the set of associated permutations Sn, applied repeatedly or in suitable combinations until the original text is reproduced. Scaling as n!, the number of possible permutations rapidly becomes intractable, and individual permutations cannot be considered for all but the smallest alphabets. This paper explores how a molecular medium, in which replication must proceed by means of template propagation, might serve to limit the number of permutations which may be reasonably find a molecular expression. The analysis suggests that the number of molecularly realisable permutations is restricted to a limited variety of permutation types, scaling linearly with alphabet size. It is also suggested that alphabets with odd numbers of letters may be less accessible than alphabets with even numbers of letters.
KeywordsEquivalence Class Original Text Artificial Life Alphabet Size Template Propagation
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