On the enumeration of d-minimal permutations

Mathilde Bouvel (1) , Luca Ferrari (2)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 DSI - Dipartimento di Sistemi e Informatica

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 discover some presumably new results concerning Eulerian numbers.

Domaines: Combinatoire [math.CO]; Mathématique discrète [cs.DM]

Mathilde Bouvel, Luca Ferrari. On the enumeration of d-minimal permutations. Discrete Mathematics and Theoretical Computer Science, 2013, 15 (2), pp.33-48. ⟨hal-00530158v2⟩