Geodesic
Word length in symmetrized presentations of Thompson's group $F$
Algebra and discrete mathematics, Tome 14 (2012) no. 2, pp. 185-216

Voir la notice de l'article provenant de la source Math-Net.Ru

Thompson's groups $F, T$ and $Z$ were introduced by Richard Thompson in the 1960's in connection with questions in logic. They have since found applications in many areas of mathematics including algebra, logic and topology, and their metric properties with respect to standard generating sets have been studied heavily. In this paper, we introduce a new family of generating sets for $F$, which we denote as $Z_n$, establish a formula for the word metric with respect to $Z_1$ and prove that $F$ has dead ends of depth at least $2$ with respect to $Z_1$.
Keywords: Thompson's group $F$, dead ends, diagram group. 
@article{ADM_2012_14_2_a4,
     author = {Matthew Horak and Alexis Johnson and Amelia Stonesifer},
     title = {Word length in symmetrized presentations of {Thompson's} group $F$},
     journal = {Algebra and discrete mathematics},
     pages = {185--216},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2012_14_2_a4/}
}
TY  - JOUR
AU  - Matthew Horak
AU  - Alexis Johnson
AU  - Amelia Stonesifer
TI  - Word length in symmetrized presentations of Thompson's group $F$
JO  - Algebra and discrete mathematics
PY  - 2012
SP  - 185
EP  - 216
VL  - 14
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2012_14_2_a4/
LA  - en
ID  - ADM_2012_14_2_a4
ER  - 
%0 Journal Article
%A Matthew Horak
%A Alexis Johnson
%A Amelia Stonesifer
%T Word length in symmetrized presentations of Thompson's group $F$
%J Algebra and discrete mathematics
%D 2012
%P 185-216
%V 14
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2012_14_2_a4/
%G en
%F ADM_2012_14_2_a4
Matthew Horak; Alexis Johnson; Amelia Stonesifer. Word length in symmetrized presentations of Thompson's group $F$. Algebra and discrete mathematics, Tome 14 (2012) no. 2, pp. 185-216. http://geodesic.mathdoc.fr/item/ADM_2012_14_2_a4/