The Use and Usefulness of Numeration Systems
The proper choice of a counting system may solve mathematical problems or lead to improved algorithms This is illustrated by a problem in combinatorial group theory, compression of sparse binary strings, encoding of contiguous binary strings of unknown lengths, ranking of permutations and combinations, strategies of games and other examples. Two abstract counting systems are given from which the concrete ones used for the applications can be derived.
KeywordsNonnegative Integer Numeration System Fibonacci Number Single Pile Huffman Code
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