A Monotonicity Property of Partial Orders
- 1 August 1981
- journal article
- research article
- Published by Wiley in Studies in Applied Mathematics
- Vol. 65 (1) , 81-83
- https://doi.org/10.1002/sapm198165181
Abstract
A proof using the FKG inequalities of the following result is obtained. Let P be a partially ordered set on a1 ⩽ a2 ⩽ ⋯ ⩽ am and b1 ⩽ b2 ⩽ ⋯ ⩽ bn. 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 ai ⩾ bj, 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 {ai} and {bj} are linearly ordered in P.Keywords
This publication has 2 references indexed in Scilit:
- Some Monotonicity Properties of Partial OrdersSIAM Journal on Algebraic Discrete Methods, 1980
- An inequality for the weights of two families of sets, their unions and intersectionsProbability Theory and Related Fields, 1978