Growing words in the free group on two generators.
Пт, 09/04/2009 - 12:10 — SomNambul
link: http://arxiv.org/abs/0909.0561
Abstract
Abstract
This paper is concerned with minimal length representatives of equivalence
classes of F_2 under Aut F_2. We give a simple inequality characterizing words
of minimal length in their equivalence class. We consider an operation that
"grows" words from other words, increasing the length, and we study root words
-- minimal words that cannot be grown from other words. Root words are "as
minimal as possible" in the sense that their characterization is the boundary
case of the minimality inequality. The property of being a root word is
respected by equivalence classes, and the length of each root word is divisible
by 4.
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