A natural generalisation of Balanced Tableaux

François Viard (1)

1 CTN - Combinatoire, théorie des nombres

We introduce the notion of ''type" that allows us to define new families of tableaux, which include both balanced and standard Young tableaux. We use these new objects to describe the set of reduced decompositions of any permutation. Moreover, we generalise the work of Edelman and Greene on balanced tableaux by giving among other things, a new proof of the fact that balanced tableaux and standard Young tableaux are equinumerous.

Mots clés: Tableaux; reduced decompositions; symmetric group; vexillary permutations

Domaines: Combinatoire [math.CO]

François Viard. A natural generalisation of Balanced Tableaux. 2014. ⟨hal-01044372v1⟩