Puzzles, Tableaux, and Mosaics

  • Date: 11/28/2006

Kevin Purbhoo (University of British Columbia)


University of British Columbia


The Littlewood-Richardson numbers show up in a number of different
areas of mathematics. They are structure constants of the ring of
symmetric functions, which connects them to representation theory and
cohomology of Grassmannians. There are now several well known
combinatorial rules for computing Littlewood-Richardson numbers. I will
talk about two of the main ones: the original rule of Littlewood and
Richardson, which is phrased in terms of tableaux, and the Knutson-Tao
'puzzle rule', which looks very different. Most every other known rule
is just a variant on one or the other. Yet it is not immediately
obvious why these two are rules are the same, or why they are correct.
I will give a new construction---mosaics---which interpolates between
puzzles and tableaux. Then a miracle will occur: just using the fact
that one can interpolate between them, a new and pleasant proof of
correctness (for both rules) will appear out of thin air.

Other Information: 

Discrete Math Seminar 2006