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  Editors-in-chief: C. A. Athanasiadis, T. Lam, A. Munemasa, H. Van Maldeghem
ISSN 0925-9899 (print) • ISSN 1572-9192 (electronic)

Determination of msd(Ln)

M. van de Vel

DOI: 10.1023/A:1018642412884


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. With computer assistance, we found that msd of the lattice {- 1, 0, 1 }4 equals 2. This value is of critical importance to determine msd of {- 1, 0, 1}n for all n ge 5 and to determine msd of the free median algebra lambda(r) for almost all r ge 5.

Pages: 161–171

Keywords: distributive lattice; free median algebra; graphic cube; median operator; median stabilization degree

Full Text: PDF


1. H.-J. Bandelt,“Generating median graphs from Boolean matrices,” Mathematisches Seminar, Universit\ddot at Hamburg (preprint).
2. H.-J. Bandelt and M. van de Vel, “The median stabilization degree of a median algebra,” Report WS-405, Vrije Universiteit Amsterdam, 1992.
3. V. Chepoi, “A multifacility location problem on median spaces,” Discrete Math. Appl. 64 (1), 1-29.
4. M. van de Vel, “Theory of convex structures,” North-Holland Math. Library, Vol. 50, Elsevier Science Publishers, Amsterdam, 1993, p. 540+xv.
5. M. van de Vel and E. Verheul, “Medians and Steiner trees,” Report WS-412, Vrije Universiteit Amsterdam, 1993.

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