Chain set of elements every two of which are

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online