“Partial Order”的概念、定义、习题解题方法及翻译-数学辞典

单词

Partial Order

释义

Partial Order

A Relation ``'' is a partial order on a Set if it has:

1. Reflexivity:

for all

2. Antisymmetry:

and

implies

3. Transitivity:

and

implies

For a partial order, the size of the longest Chain (Antichain) is called the Length (Width). A partially ordered set is also called a Poset.

See also Antichain, Chain, Fence Poset, Ideal (Partial Order), Length (Partial Order),Linear Extension, Partially Ordered Set, Total Order, Width (Partial Order)

References

Ruskey, F. ``Information on Linear Extension.'' http://sue.csc.uvic.ca/~cos/inf/pose/LinearExt.html.

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