Order

, Volume 17, Issue 3, pp 287–299 | Cite as

Singular Points and an Upper Bound of Medians in Upper Semimodular Lattices

  • Jinlu Li
  • Kaddour Boukaabar
Article

Abstract

Given a k-tuple P=(x1,x2,...,xk) in a finite lattice X endowed with the lattice metric d, a median of P is an element m of X minimizing the sum ∑id(m,xi). If X is an upper semimodular lattice, Leclerc proved that a lower bound of the medians is c(P), the majority rule and he pointed out an open problem: “Is c1(P)=∨ixi, the upper bound of the medians?” This paper shows that the upper bound is not c1(P) and gives the best possible upper bound.

majority rule median semimodular lattice singular point 

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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Jinlu Li
    • 1
  • Kaddour Boukaabar
    • 2
  1. 1.Department of MathematicsShawnee State UniversityPortsmouth
  2. 2.Department of Mathematics and Computer ScienceCalifornia University of PennsylvaniaCaliforniaU.S.A.

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