Interesting Esoterica

The Curling Number Conjecture

Article by Benjamin Chaffin and N. J. A. Sloane
  • Published in 2009
  • Added on
In the collection
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. The conjecture remains open, but we will report on some numerical results and conjectures in the case when S consists of only 2's and 3's.

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BibTeX entry

@article{TheCurlingNumberConjecture,
	title = {The Curling Number Conjecture},
	abstract = {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. The conjecture remains open, but we will report on some
numerical results and conjectures in the case when S consists of only 2's and
3's.},
	url = {http://arxiv.org/abs/0912.2382v5 http://arxiv.org/pdf/0912.2382v5},
	author = {Benjamin Chaffin and N. J. A. Sloane},
	comment = {},
	urldate = {2017-07-31},
	archivePrefix = {arXiv},
	eprint = {0912.2382},
	primaryClass = {math.CO},
	year = 2009,
	collections = {easily-explained}
}