Geodesic
The symmetries of McCullough--Miller space
Algebra and discrete mathematics, Tome 14 (2012) no. 2, pp. 239-266.

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

We prove that if $W$ is the free product of at least four groups of order $2$, then the automorphism group of the McCullough-Miller space corresponding to $W$ is isomorphic to group of outer automorphisms of $W$. We also prove that, for each integer $n \geq 3$, the automorphism group of the hypertree complex of rank $n$ is isomorphic to the symmetric group of rank $n$.
Keywords: Autmorphisms of groups; group actions on simplicial complexes; Coxeter groups; McCullough-Miller space; hypertrees. 
@article{ADM_2012_14_2_a8,
     author = {Adam Piggott},
     title = {The symmetries of {McCullough--Miller} space},
     journal = {Algebra and discrete mathematics},
     pages = {239--266},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2012_14_2_a8/}
}
TY  - JOUR
AU  - Adam Piggott
TI  - The symmetries of McCullough--Miller space
JO  - Algebra and discrete mathematics
PY  - 2012
SP  - 239
EP  - 266
VL  - 14
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2012_14_2_a8/
LA  - en
ID  - ADM_2012_14_2_a8
ER  - 
%0 Journal Article
%A Adam Piggott
%T The symmetries of McCullough--Miller space
%J Algebra and discrete mathematics
%D 2012
%P 239-266
%V 14
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2012_14_2_a8/
%G en
%F ADM_2012_14_2_a8
Adam Piggott. The symmetries of McCullough--Miller space. Algebra and discrete mathematics, Tome 14 (2012) no. 2, pp. 239-266. http://geodesic.mathdoc.fr/item/ADM_2012_14_2_a8/

[1] The On-Line Encyclopedia of Integer Sequences, Published electronically at , 2011 http://oeis.org

[2] M. R. Bridson, K. Vogtmann, “The symmetries of outer space”, Duke Math. J., 106:2 (2001), 391–409 | DOI | MR | Zbl

[3] N. D. Gilbert, “Presentations of the automorphism group of a free product”, Proc. London Math. Soc. (3), 54:1 (1987), 115–140 | DOI | MR | Zbl

[4] L. Kalikow, Enumeration of parking functions, allowable permutation pairs, and labeled trees, PhD thesis, Brandeis University, 1999 | MR

[5] J. McCammond, J. Meier, “The hypertree poset and the $l^2$-Betti numbers of the motion group of the trivial link”, Math. Ann., 328:4 (2004), 633–652 | DOI | MR | Zbl

[6] D. McCullough, A. Miller, Symmetric automorphisms of free products, Mem. Amer. Math. Soc., 122, no. 582, 1996 | MR

[7] D. Warme, Spanning trees in hypergraphs with applications to Steiner trees, PhD thesis, University of Virginia, 1998 | MR