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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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 Fall '08
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