On the enumeration of d-minimal permutations

2010/10/28 by Bouvel, Mathilde, Ferrari, Luca
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics

paper · doi:10.48550/arxiv.1010.5963

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 discover some presumably new results concerning Eulerian numbers.

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• Minimal Permutations and 2-Regular Skew Tableaux
• Enumeration formulas for Young tableaux in a diagonal strip
• Canon permutations and generalized descents of standard Young tableaux
• Refined Eulerian numbers and ballot permutations
• Dyck Paths, Standard Young Tableaux, and Pattern Avoiding Permutations