A Catalogue of Combinatorial Geometries

Abstract

We include in the microfiche section of this issue a catalogue of all the different geometric configurations which may be constructed from zz points, zz S 8, by specifying their points, lines, planes, . . ., colines, copoints, their flats of each rank.It suffices to list the copoints of each combinatorial geometry G, because the colines of G are the copoints of a geometry earlier in the list, which may be located by deleting one component of the designator of G. Introduction.We list, in the microfiche section of this issue, all the different geometrical configurations which may be constructed with zz points, zz g 8.Combinatorial geometries [2] are very general, including the projective, affine, and Möbius (etc.)geometries over various fields, any subgeometry (determined by a subset of the set of points) of such a geometry, as well as many geometries that are not so representable.The flats of a combinatorial geometry satisfy the following simple axioms: Each flat is a set of points, the empty set 0 and the one-point sets are flats, any intersection of flats is a flat, and the points not in a flat Y (of rank k, say) are partitioned by inclusion in the flats of

Locations

• Mathematics of Computation - View - PDF