Construire des diagrammes de Young (avec des rectangles via les partitions régulières)

Résumé

One can naturally tile a Young diagram by horizontal rectangles, and the dual partition gives a tiling by vertical rectangles. Both points of view are used with Frobenius coordinates, which give a tiling of the Young diagram with horizontal (resp. vertical) rectangles above (resp. below) the diagonal. In this talk, we propose a way to tile a Young diagram where horizontal and vertical tiles are mixed. The tiling for an (e1)(e1)-tuple of partitions is given by a certain ee-regular partition, via a “caterpillar” reading of the ee-abacus. One can recover the e-regular partition from the (e1)(e1)-tuple of partitions via nested e-regularisations for e2,3,,e.

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CIRM