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Counting words of minimum length in an automorphic orbit, in preparation
| Citations: | 9 - 2 self |
BibTeX
@MISC{Lee_countingwords,
author = {Donghi Lee},
title = {Counting words of minimum length in an automorphic orbit, in preparation},
year = {}
}
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Abstract
Abstract. Let u be a cyclic word in a free group Fn of finite rank n that has the minimum length over all cyclic words in its automorphic orbit, and let N(u) be the cardinality of the set {v: |v | = |u | and v = φ(u) for some φ ∈ AutFn}. In this paper, we prove that N(u) is bounded by a polynomial function with respect to |u | under the hypothesis that if two letters x, y occur in u, then the total number of x and x −1 occurring in u is not equal to the total number of y and y −1 occurring in u. A complete proof without the hypothesis would yield the polynomial time complexity of Whitehead’s algorithm for Fn. 1.
