Jean-Christophe Aval

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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)
In this work, we put to light a formula that relies the number of fully packed loop configurations (FPLs) associated to a given coupling π to the number of half-turn symmetric FPLs (HTFPLs) of even size whose coupling is a punctured version of the coupling π. When the coupling π is the coupling with all arches parallel π 0 (the " rarest " one), this formula(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'´ enumérer les matrices` a signes(More)