A unified proof of the Bridges and de Witte theorems and of the fundamental theorem of finite linear spaces (Q1864680)
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scientific article; zbMATH DE number 1884299
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A unified proof of the Bridges and de Witte theorems and of the fundamental theorem of finite linear spaces |
scientific article; zbMATH DE number 1884299 |
Statements
A unified proof of the Bridges and de Witte theorems and of the fundamental theorem of finite linear spaces (English)
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18 March 2003
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A classical result due to \textit{N. G. de Bruijn} and \textit{P. Erdős} [Indag. Math. 10, 421-423 (1948)] states that in a finite linear space the number of lines is greater than or equal to the number of points. Finite linear spaces with \(v\) points and \(v+1\) lines were classified by \textit{W. G. Bridges} [J. Comb. Theory, Ser. A 13, 116-126 (1972; Zbl 0264.05015)], and finite linear spaces with \(v\) points and \(v+2\) lines were classified by \textit{P. de Witte} [J. Reine Angew. Math. 288, 66-73 (1976; Zbl 0333.50009)]. Using elementary counting arguments, the author proposes a unified and short proof of the classical results mentioned above.
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linear incidence geometries
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