Bulletin of the Korean Mathematical Society (대한수학회보)
- Volume 32 Issue 2
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- Pages.215-219
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- 1995
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- 1015-8634(pISSN)
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- 2234-3016(eISSN)
A CHARACTERIZATION OF PROJECTIVE GEOMETRIES
Abstract
The most fundamental examples of (combinatorial) geometries are projective geometries PG(n - 1,q) of dimension n - 1, representable over GF(q), where q is a prime power. Every upper interval of a projective geometry is a projective geometry. The Whitney numbers of the second kind are Gaussian coefficients. Every flat of a projective geometry is modular, so the projective geometry is supersolvable in the sense of Stanley [6].