Geodesic
The median stabilization degree of a median algebra
Journal of Algebraic Combinatorics, Tome 9 (1999) no. 2, pp. 115-127.

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Summary: The median stabilization degree (msd, for short) of a median algebra measures the largest possible number of steps needed to generate a subalgebra with an arbitrary set of generators. We determine the value of msd of a graphic n-cube Qn and we derive an estimation of msd for the natural median operator of Rn which is sharp up to one or two units. Interestingly, msd of Qn and of Rn grows like log1.5n. Finally, we characterize median algebras and median graphs of msd $le$ 1 in terms of forbidden subspaces.
Keywords: convex structure, graphic cube, median algebra, median stabilization degree, superextension 
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     author = {Bandelt, H.-J. and van de Vel, M.},
     title = {The median stabilization degree of a median algebra},
     journal = {Journal of Algebraic Combinatorics},
     pages = {115--127},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_1999__9_2_a6/}
}
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Bandelt, H.-J.; van de Vel, M. The median stabilization degree of a median algebra. Journal of Algebraic Combinatorics, Tome 9 (1999) no. 2, pp. 115-127. http://geodesic.mathdoc.fr/item/JAC_1999__9_2_a6/