Algorithms and combinatorics of maximal compact codes

The implementation of two different algorithms for generating compact codes of some size N are presented. An analysis of both algorithms is given, in an attempt to prove whether or not the algorithms run in constant amortized time. Meta-Fibonacci sequences are also investigated in this paper. Using a particular numbering on k-ary trees, we find that a group of meta-Fibonacci sequences count the number of nodes at the bottom level of these k-ary trees. These meta-Fibonacci sequences are also related to compact codes. Finally, generating functions are proved for the meta-Fibonacci sequences discussed.