Jean-Christophe Aval

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In this work we introduce and study tree-like tableaux, which are certain fillings of Ferrers diagrams in simple bijection with permutation tableaux and alternative tableaux. We exhibit an elementary insertion procedure on our tableaux which gives a clear proof that tree-like tableaux of size n are counted by n!, and which moreover respects most of the(More)
The aim of this work is to enumerate alternating sign matrices (ASM) that are quasi-invariant under a quarter-turn. The enumeration formula (conjectured by Duchon) involves, as a product of three terms, the number of unrestricted ASM’s and the number of half-turn symmetric ASM’s. Résumé. L’objet de ce travail est d’énumérer les matrices à signes alternants(More)
Let μ = (μ1 ≥ μ2 ≥ · · · ≥ μk > 0) be a partition of n. We shall identify μ with its Ferrers diagram (using the French notation). To each cell s of the Ferrers diagram, we associate its coordinates (i, j), where i is the height of s and j the position of s in its row. The pairs (i − 1, j − 1) occurring while s describes μ will be briefly referred to as the(More)
In [12], Lascoux and Schützenberger introduced a notion of key associated to any Young tableau. More recently Lascoux defined the key of an alternating sign matrix by recursively removing all −1’s in such matrices. But alternating sign matrices are in bijection with monotone triangles, which form a subclass of Young tableaux. We show that in this case these(More)
are integers that appear in many combinatorial problems. These numbers first arose in the work of Catalan as the number of triangulations of a polygon by mean of nonintersecting diagonals. Stanley [13, 14] maintains a dynamic list of exercises related to Catalan numbers, including (at this date) 127 combinatorial interpretations. Closely related to Catalan(More)
A lattice diagram is a finite set L = {(p1, q1), . . . , (pn, qn)} of lattice cells in the positive quadrant. The corresponding lattice diagram determinant is ∆L(Xn;Yn) = det ‖ x pj i y qj i ‖. The space ML is the space spanned by all partial derivatives of ∆L(Xn;Yn). We denote by M 0 L the Y -free component of ML. For μ a partition of n + 1, we denote by(More)
The starting point of this work is the discovery of a new and direct construction that relies bijectively the permutations of length n to some weighted Dyck paths named subdivided Laguerre histories. These objects correspond to the combinatorial interpretation of the development of the generating function for factorial numbers in terms of a Stieltjes(More)
We obtain explicit formulas for the enumeration of labelled parallelogram polyominoes. These are the polyominoes that are bounded, above and below, by northeast lattice paths going from the origin to a point (k, n). The numbers from 1 to n (the labels) are bijectively attached to the n north steps of the above-bounding path, with the condition that they(More)