The Robinson–Schensted correspondence for skew oscillating semi-standard tableaux

Properties of the Robinson-schensted Correspondence for Oscillating and Skew Oscillating Tableaux

In this paper, we consider the Robinson-Schensted correspondence for oscillating tab-leaux and skew oscillating tableaux deened in 15] and 3]. First we give an analogue, for the oscillating tableaux, of the classical geometric construction of Viennot for standard tableaux ((16]). Then, we extend a construction of Sagan and Stanley ((10]), dealing with standard tableaux and skew tableaux, to ded...

A geometric version of the Robinson-Schensted correspondence for skew oscillating tableaux

Enumeration of Semi { Standard Young Tableaux

Standard tableaux. A Young tableau (also known as a standard tableau) is an arrangement of distinct integers in an array of left justiied rows, such that the entries of each row are in increasing order from left to right and the entries of each column are in increasing order from bottom to top 2. For instance, here is an array of size 15: 11 4 8 12 14 3 6 7 13 1 2 5 9 10 15 : In general a table...

Descent sets for oscillating tableaux

The descent set of an oscillating (or up-down) tableau is introduced. This descent set plays the same role in the representation theory of the symplectic groups as the descent set of a standard tableau plays in the representation theory of the general linear groups. In particular, we show that the descent set is preserved by Sundaram’s correspondence. This gives a direct combinatorial interpret...

Oscillating tableaux and a superanalogue of the Robinson-Schensted-Knuth correspondence

In this paper, we investigate the super RSK correspondence, first introduced by Pak and Postnikov (1994), which generalizes both the RSK correspondence and the dual RSK correspondence. The bijection relates objects that are known as oscillating supertableau and (intransitive) supergraphs. We prove a number of theorems that were stated in the original paper of Pak and Postnikov, but whose proofs...