In this paper, we show that the full algebraic combinatorial geometry is not a projective geometry, it is only semimodular, but the p-polynomial points give a projective subgeometry. Also, we show that the subgeometry can be coordinatized by a skew field, which is quotient ring of an Ore domain. As
On the nonreconstructibility of combinatorial geometries
β Scribed by Tom Brylawski
- Publisher
- Elsevier Science
- Year
- 1975
- Tongue
- English
- Weight
- 269 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0095-8956
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π SIMILAR VOLUMES
In [4], line-closed combinatorial geometries were studied. Here, given a line-closed combinatorial geometry G(X), we determine all single point extensions of G(X) that are line-closed. Further, if H(X U r) is a line-closed geometry that is a smooth extension of G(X) we give a natural necessary and s
Let us fix a number a, O< a < 2. We join two p0int.s on the unit sphere Sm in the real m-space iff their distance is a. Denote the obtained graph by g,,,. We prove that the chromatic number x(9@,,,) tends to infinity when m --+ a. This gives a positive answer to a question of P. Erdiis.
A hereditary class 24 Β° of combinatorial geometries (or simple matroids) is a collection of geometries closed under minors and direct sums. A geometry G in ~ is extremal if no proper extension of G of the same rank is in Yr. The size function h(n) of ~ is defined by h(n)-max{[G[:GEgf and rank(G)-n},