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Summer 2011 Growing words in the free group on two generators
Bobbe Cooper, Eric Rowland
Illinois J. Math. 55(2): 417-426 (Summer 2011). DOI: 10.1215/ijm/1359762395


This paper is concerned with minimal-length representatives of equivalence classes of words in $F_2$ 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 minimal 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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Bobbe Cooper. Eric Rowland. "Growing words in the free group on two generators." Illinois J. Math. 55 (2) 417 - 426, Summer 2011.


Published: Summer 2011
First available in Project Euclid: 1 February 2013

zbMATH: 1279.20037
MathSciNet: MR3020689
Digital Object Identifier: 10.1215/ijm/1359762395

Primary: 20E05, 68R15

Rights: Copyright © 2011 University of Illinois at Urbana-Champaign


Vol.55 • No. 2 • Summer 2011
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