Linear extension: Difference between revisions

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== Algebraic combinatorics ==

Counting the number of linear extensions of a finite poset is a common problem in [[algebraic combinatorics]]. This number is given by the leading coefficient of the [[order polynomial]] multiplied by |P|!.

[[Young tableau]] can be considered as linear extensions of a finite [[Ideal (order theory)|order-ideal]] in the infinite poset <math>\mathbb{N}\times\mathbb{N}</math>, and they are counted by the [[hook length formula]].

== References ==