A Monotonicity Property of Partial Orders | Zendy

Kleitman D. J. | Zendy; Shearer J. B. | Zendy

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A Monotonicity Property of Partial Orders

Author(s) -

Kleitman D. J.,

Shearer J. B.

Publication year - 1981

Publication title -

studies in applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 46

eISSN - 1467-9590

pISSN - 0022-2526

DOI - 10.1002/sapm198165181

Subject(s) - monotonic function , mathematics , combinatorics , property (philosophy) , partially ordered set , set (abstract data type) , order (exchange) , discrete mathematics , mathematical analysis , philosophy , epistemology , computer science , programming language , finance , economics

A proof using the FKG inequalities of the following result is obtained. Let P be a partially ordered set on a 1 ⩽ a 2 ⩽ ⋯ ⩽ a m and b 1 ⩽ b 2 ⩽ ⋯ ⩽ b n . Let P ( x ) be the proportion of linear extentions of P for which x holds. If x and y are disjunctions of conjunctions of additional inequalities of the form a i ⩾ b j , then P ( x and y ) ⩾ P ( x ) P ( y ). An example is provided that shows the result can be false if we don't assume the { a i } and { b j } are linearly ordered in P .

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