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All erections of a combinatorial geometry and their automorphism groups

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Part of the Lecture Notes in Mathematics book series (LNM,volume 452)

Abstract

We obtain all erections of an arbitrary combinatorial geometry from a simply specified collection of subsets of the underlying set and express the automorphism group of each in terms of this collection of subsets and the automorphism group of the original geometry.

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Bibliography

  1. H.H. Crapo, Erecting geometries, Ann. New York Acad. Sci. 175 (1970), 89–92.

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  2. H.H. Crapo and G.-C. Rota, On the Foundations of Combinatorial Theory: Combinatorial Geometries (preliminary edition, M.I.T. Press, Cambridge, Massachusetts and London, England, 1970).

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  3. L.A. Roberts, Characterisation of a pregeometry by its flats, Combinatorial Mathematics: Proc. Second Australian Conference, Lecture Notes in Math. Vol. 403, Springer-Verlag, Berlin, Heidelberg, New York, (1974), to appear.

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© 1975 Springer-Verlag

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Roberts, L. (1975). All erections of a combinatorial geometry and their automorphism groups. In: Street, A.P., Wallis, W.D. (eds) Combinatorial Mathematics III. Lecture Notes in Mathematics, vol 452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069559

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  • DOI: https://doi.org/10.1007/BFb0069559

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07154-9

  • Online ISBN: 978-3-540-37482-4

  • eBook Packages: Springer Book Archive