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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 <math>|P|!.</math>
[[Young diagram]]s can be considered a finite [[Ideal (order theory)|order-ideal]] in the infinite poset <math>\N \times \N</math>. Similarly, [[Young tableau|standard Young tableaux]] can be considered as linear extensions of a poset corresponding to the Young diagram. For the (usual) Young diagrams, linear extensions are counted by the [[hook length formula]]. For the skew Young diagrams, linear extensions are counted by a determinantal formula.<ref>Chan, S.H.;
==References==
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