Dyck tableaux

We introduce and study new combinatorial objects called Dyck tableaux which may be seen as a variant of permutation tableaux. These objects appear in the combinatorial interpretation of the physical model PASEP (Partially Simple Asymmetric Exclusion Process). Dyck tableaux afford a simple recursive structure through the construction of an insertion algorithm. With this tool, we are able to describe statistics which are relevant in the PASEP model, in a more direct way than in previous works. Moreover, we give a new and natural link between permutations and certain labeled Dyck paths known as subdivided Laguerre histories.