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Published online by Cambridge University Press: 24 October 2008
The problem of finding the number of r-dimensional regions which are situated in a space Sn of n dimensions, and which satisfy a suitable number of conditions of certain assigned types (called “ground-conditions”) has been investigated by Schubert. A special class of such problems arises when the r-dimensional region is merely required to intersect k regions Pλ of rλ dimensions (λ = 1, 2 … k) situated in general position in Sn where for the finiteness of the sought number we must have
† Math. Annalen, Bd. 26, 38.
‡ For an account of this principle see Schubert, Kalkul der Abzahlenden Geometric, or preferably Zeuthen, “Abzahlenden Methoden” (Ency. Math. Wiss.).
§ Math. Annalen, Bd. 59.
