aequationes mathematicae

, Volume 16, Issue 1–2, pp 37–50 | Cite as

Uniform binary geometries

  • Martin Aigner
Research papers


In a geometric lattice every interval can be mapped isomorphically into an upper interval (containing 1) by a strong map. A natural question thus arises as to what extent certain assumptions on the “upper interval structure” determine the whole lattice. We consider conditions of the following sort: that above a certain levelm any two upper intervals of the same length be isomorphic. This property, called uniformity, is studied for binary geometries. The geometries satisfying the strongest uniformity condition (m = 1) are determined (except for one open case). As is to be expected the corresponding problem for lower intervals is easier and is solved completely.

AMS (1970) subject classification

Primary 05B25, 05B35 Secondary 06A25, 06A30 


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Copyright information

© Birkhäuser Verlag 1977

Authors and Affiliations

  • Martin Aigner
    • 1
  1. 1.II. Mathematisches InstitutFreie Universität Berlin1 Berlin 33Germany

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