The Curling Number Conjecture

Details The Curling Number Conjecture The Curling Number Conjecture

2009-12-12

arxiv.org/abs/0912.2382v3

Mathematics

Combinatorics

4 pages. Dec 17 2009 fixed a typo. Feb 18 2010: added Ben Chaffin as coauthor, many new results

Scientific paper

Given a finite nonempty sequence of integers S, by grouping adjacent terms it is always possible to write it, possibly in many ways, as S = X Y^k, where X and Y are sequences and Y is nonempty. Choose the version which maximizes the value of k: this k is the curling number of S. The curling number conjecture is that if one starts with any initial sequence S, and extends it by repeatedly appending the curling number of the current sequence, the sequence will eventually reach 1.

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