Abstract
By a system we will mean a finite sequence S 1,..., S m of finite sets of positive integers. Denote by (a, i) the occurrence of integer a in set S i. The scope of (a, i) is the union of the sets S α with j ≤ α ≤ k, where 1 ≤ j ≤ i ≤ k ≤ m and j is as low and k is as high as possible subject to the condition that for all β satisfying j < β < k, one has a ∈ S β. This means that the scope consists of the sets in the run of a’s to which (a, i) belongs, extended at each end of the run by one additional set, unless that end of the run is one end of the system.
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H.S. Witsenhausen, “On Woodall’s Interval Problem,” J. Combinatorial Theory, Ser. A, 21, pp. 222–229 (1976).
D.R. Woodall, “Problem No. 4,” Combinatorics, London Mathematics Society Lecture Note Series, No. 13, Cambridge Universitiy Press, Cambridge, 1974, p. 202.
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© 1987 Springer-Verlag New York Inc.
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Witsenhausen, H.S. (1987). The Scope Problem. In: Cover, T.M., Gopinath, B. (eds) Open Problems in Communication and Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4808-8_34
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DOI: https://doi.org/10.1007/978-1-4612-4808-8_34
Publisher Name: Springer, New York, NY
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