Combinatorics of diagrams of permutations

Combinatorics of diagrams of permutations

There are numerous combinatorial objects associated to a Grassmannian permutationwλ that index cells of the totally nonnegative Grassmannian. We study some of these objects (rook placements, acyclic orientations, various restricted fillings) and their q-analogues in the case of permutations w that are not necessarily Grassmannian. Résumé. Il y a nombreaux objets combinatoires associés à une per...

On Additive Combinatorics of Permutations of ℤn

Let Zn denote the ring of integers modulo n. A permutation of Zn is a sequence of n distinct elements of Zn. Addition and subtraction of two permutations is defined element-wise. In this paper we consider two extremal problems on permutations of Zn, namely, the maximum size of a collection of permutations such that the sum of any two distinct permutations in the collection is again a permutatio...

Analytic Combinatorics of Chord Diagrams Analytic Combinatorics of Chord Diagrams Combinatoire Analytique Des Diagrammes De Cordes Analytic Combinatorics of Chord Diagrams

In this paper we study the enumeration of diagrams of n chords joining 2n points on a circle in disjoint pairs. We establish limit laws for the following three parameters: number of components, size of the largest component, and number of crossings. We also nd exact formulas for the moments of the distribution of number of components and number of crossings. Key-words: Analytic combinatorics, c...

Diagrams of Affine Permutations and Their Labellings

We study affine permutation diagrams and their labellings with positive integers. Balanced labellings of a Rothe diagram of a finite permutation were defined by FominGreene-Reiner-Shimozono, and we extend this notion to affine permutations. The balanced labellings give a natural encoding of the reduced decompositions of affine permutations. We show that the sum of weight monomials of the column...

Review of: Combinatorics of Permutations by MiklÃ3s BÃ3na