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On the number of planes in hyperspace which satisfy a certain set of conditions
Published online by Cambridge University Press: 24 October 2008
Extract
The problem here considered is a particular case of the more general problem of finding the number of [k]s, lying in a space of dimension n(n > k), which satisfy a certain number of conditions of the following type: viz. to meet a given [a0] in a point, a given, [a1] containing the [a0], in a line, etc., finally to lie in a given [ak] containing [ak−1]. The number of such conditions is such that there are just a finite number of [k]s which satisfy them all. The method which we employ is the one introduced by Schubert and commonly known as the “degeneration method” it is explained very briefly below.
- Type
- Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 25 , Issue 1 , January 1929 , pp. 42 - 47
- Copyright
- Copyright © Cambridge Philosophical Society 1929
References
* We denote as usual by [k] a. flat space of k dimensions.
† Schubert, , Kalkül der Abzählende Geometrie, Leipzig, 1879.Google Scholar
‡ Bertini, , Introduzione alla geometria proiettiva degli iperspazi (1923), p. 39.Google Scholar
§ Bertini, , loc. cit. p. 38.Google Scholar
* Bertini, , loc. cit. p. 254.Google Scholar
† Bertini, , loc. cit. Chap. 4.Google Scholar
* Encyk. der Math. Wiss. III C 7, p. 817, footnote 157.Google Scholar
† Mem. Acc. Torino (2), 52 (1902), p. 171.Google Scholar
‡ I am indebted to Mr W. R. Andress for this remark.