Highly Influenced

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@article{Graham1979SomeMP, title={Some Monotonicity Properties of Partial Orders}, author={Ronald L. Graham and Andrew Chi-Chih Yao and F. Frances Yao}, journal={SIAM J. Matrix Analysis Applications}, year={1979}, volume={1}, pages={251-258} }

- Published in SIAM J. Matrix Analysis Applications 1979
DOI:10.1137/0601028

A fundamental quantity which arises in the sorting of n numbers al, a2.''", an is Pr (ai < ai]P), the probability that ai < ai assuming that all linear extensions of the partial order P are equally likely. In this paper, we establish various properties of Pr (ai < ajlP) and related quantities. In particular, it is shown that Pr (ai <bjlP')>=Pr (a<b.iP) if the partial order P consists of two disjoint linearly ordered sets A ={al<a2<" "<a,,,,},B={bl<b2<" '<bn} and P'=PU{any relations of the form… CONTINUE READING