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- W2055141195 abstract "Dilworth's theorem gives the number of chains whose union is a given partially ordered set in terms of intrinsic properties of the partial ordering. This paper uses Dilworth's theorem to find the number of chains needed to uniquely determine a given partially ordered set in terms of intrinsic properties of the partial ordering. If a covers b and c covers d, then (a, b) and (c, d) are incomparable covers if either a or b is incomparable with either c or d. We prove that the number of chains whose transtitive closure is a given partial ordering is the largest number of elements in any set of incomparable covers plus the number of isolated elements of the partially ordered set." @default.
- W2055141195 created "2016-06-24" @default.
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- W2055141195 date "1970-07-01" @default.
- W2055141195 modified "2023-09-25" @default.
- W2055141195 title "Decomposing partial orderings into chains" @default.
- W2055141195 cites W1970064177 @default.
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- W2055141195 doi "https://doi.org/10.1016/s0021-9800(70)80059-x" @default.
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