Definitions
Given any partial orders ≤ and ≤* on a set X, ≤* is a linear extension of ≤ exactly when (1) ≤* is a linear order and (2) for every x and y in X, if x ≤ y, then x ≤* y. It is that second property that leads mathematicians to describe ≤* as extending ≤.
Alternatively, a linear extension may be viewed as an order-preserving bijection from a partially ordered set P to a chain C on the same ground set.
Read more about this topic: Linear Extension
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