Uniform binary geometries |
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Authors: | Martin Aigner |
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Affiliation: | (1) II. Mathematisches Institut, Freie Universität Berlin, 1 Berlin 33, Germany |
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Abstract: | 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. |
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Keywords: | Primary 05B25, 05B35 Secondary 06A25, 06A30 |
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