BIT Numerical Mathematics

, Volume 9, Issue 2, pp 97–118 | Cite as

Algorithms over partially ordered sets

  • R. M. Baer
  • O. Østerby


We here study some problems concerned with the computational analysis of finite partially ordered sets. We begin (in § 1) by showing that the matrix representation of a binary relationR may always be taken in triangular form ifR is a partial ordering. We consider (in § 2) the chain structure in partially ordered sets, answer the combinatorial question of how many maximal chains might exist in a partially ordered set withn elements, and we give an algorithm for enumerating all maximal chains. We give (in § 3) algorithms which decide whether a partially ordered set is a (lower or upper) semi-lattice, and whether a lattice has distributive, modular, and Boolean properties. Finally (in § 4) we give Algol realizations of the various algorithms.


Computational Mathematic Matrix Representation Computational Analysis Chain Structure Maximal Chain 
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Copyright information

© BIT Foundations 1969

Authors and Affiliations

  • R. M. Baer
    • 1
    • 2
  • O. Østerby
    • 1
    • 2
  1. 1.Computer CenterUniversity of CaliforniaBerkeleyUSA
  2. 2.Matematisk InstitutÅrhus UniversitetÅrhusDenmark

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