Abstract

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 $(e − 1)$-tuple of partitions is given by a certain $e$-regular partition, via a “caterpillar” reading of the $e$-abacus. One can recover the e-regular partition from the $(e − 1)$-tuple of partitions via nested $e’$-regularisations for $e’ \in {2,3,\dots,e}$.