Partial Orders, Sperner k-families, RSK and Tableaux Pairs: A collision of labels.
by Dr. Richard Brak
Abstract: Curtis Green's duality theorem maps an arbitrary finite poset to an integer partition.
In the special case of a permutation poset it provides a combinatorial interpretation of the rows
and columns of the insertion partition arising from the RSK bijection between permutations and pairs of partitions. I will introduce a association between posets and a partial order on distinct intervals on the integer line [-n,n] which leads to a new algorithm, via an "unshuffle" operation, for producing
the duality map (actually it produces a pair of tableaux). In the special case of permutation posets
this provides (yet another) way of constructing the RKS bijection. Interestingly, in the permutation case, the unshuffle operation gives a different way of constructing Fomin's growth algorithms for partitions.
Note, this is very much work-in-progress and hence will highlight the various pros and cons of talking about WIP.
For More Information: Dr. Iwan Jensen I.Jensen@ms.unimelb.edu.au