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.
On the enumeration of d-minimal permutations / Mathilde Bouvel; Luca Ferrari. - In: DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE. - ISSN 1365-8050. - ELETTRONICO. - 15 (2):(2013), pp. 33-48.
On the enumeration of d-minimal permutations
FERRARI, LUCA
2013
Abstract
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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