Discrete Mathematics & Theoretical Computer Science, Vol 15, No 2 (2013)

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On the enumeration of d-minimal permutations

Mathilde Bouvel, Luca Ferrari


We suggest an approach for the enumeration of minimal permutations having d descents which uses skew Young tableaux. We succeed in finding a general expression for the number of such permutations in terms of (several) sums of determinants. We then generalize the class of skew Young tableaux under consideration; this allows in particular to recover a formula for Eulerian numbers which is a direct consequence of a result of MacMahon.

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