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- W2045940527 abstract "We consider the lattice of subspaces of an n -dimensional vector space V n q over a finite field GF ( q ) and represent a family of such subspaces by elements of a set X . The q -analog of the principle of inclusion–exclusion expresses the size of the union of elements of X representing subspaces of V n q in terms of the sizes of subsets of X whose intersection contains a given subspace of V n q . We study the problem of approximating the size of this union when intersection sizes are known only for some subspaces of V n q . In particular, we consider the case where intersection sizes are given for subsets of X whose intersection contains a subspace of V n q of dimension at most k . We extend methods of Linial and Nisan (1990, Combinatorica 10 , No. 4, pp. 349–365), drawn from approximation theory, to show that the quality of approximation changes in a significant way around [equation]: if [equation], then any approximation may err by a factor of [equation]; while if [equation] , the size of the union may be approximated to within a multiplicative factor of [equation]. Our result, the first q -analog of a computational property of the lattice of subsets of a finite set, answers in the affirmative a question posed by Linial and Nisan." @default.
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- W2045940527 date "1998-01-01" @default.
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- W2045940527 title "Aq-Analog of Approximate Inclusion–Exclusion" @default.
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- W2045940527 doi "https://doi.org/10.1006/aama.1997.0568" @default.
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