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# Chain set of elements every two of which are

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Unformatted text preview: lete isoforms. 14 Dilworth’s Theorem: characterizes the width of any parEally ordered set in terms of a parEEon of the order into a minimum number of chains 15 ParEally Ordered Set •  Par>ally ordered set (or poset) formalizes and generalizes the intuiEve concept of an ordering, sequencing, or arrangement of the elements of a set. Poset = Set + Binary RelaEon 16 AnEchain and Poset Width •  We say two elements a and b of a parEally ordered set are comparable if a ≤ b or b ≤ a. •  Chain: set of elements every two of which are comparable. •  An>chain: subset of a parEally ordered set such that any two elements in the subset are incomparable. •  Width of a poset: the cardinality of a maximum anEchain. 17 Dilworth’s Theorem: characterizes the width of any parEally ordered set in terms of a parEEon of the order into a minimum number of chains 18 Dilworth’s Theorem •  Dilworth's Theorem: the number o...
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