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Fishburn–Shepp inequality : ウィキペディア英語版
Fishburn–Shepp inequality
In combinatorial mathematics, the Fishburn–Shepp inequality is an inequality for the number of extensions of partial orders to linear orders, found by and .
It states that if ''x'', ''y'', and ''z'' are incomparable elements of a finite poset, then
: P(x
where ''P''(
*) is the probability that a linear order < extending the partial order has the property
*.
In other words the probability that ''x'' < ''z'' strictly increases if one adds the condition that ''x'' < ''y''. In the language of conditional probability,
: P(x < z) < P(x < z \mid x < y).\,
The proof uses the Ahlswede–Daykin inequality.
==References==

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抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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