f-number

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f-number

, f number
Photog the numerical value of the relative aperture. If the relative aperture is f8, 8 is the f-number and indicates that the focal length of the lens is 8 times the size of the lens aperture
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The most natural combinatorial invariant of a finite (d - 1)-dimensional simplicial poset is its f-vector, f (P) := ([f.sub.-1] (P), [f.sub.0] (P), ..., [f.sub.d-1] (P)), where the f-numbers [f.sub.i] (P) count the number of i-dimensional faces in P.
Kruskal (1963) and Katona (1968) gave a complete classification of f-vectors of simplicial complexes, by establishing nonlinear inequalities that bound the relative growth of successive f-numbers. In contrast, Stanley (1991) showed that the only condition that is required on the f-numbers of a simplicial poset of rank d is that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]: that is to say that such a simplicial poset must contain a face of dimension d - 1, which in turn contains [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] faces of dimension i; but there are no further restrictions on the f-numbers.