Abstract :

Young tableaux are certain combinatorial objects introduced in relation with some considerations in algebra. Pairs of Young tableaux with the same "shape" are enumerated by n! , that is the number of permutations on n elements. A famous correspondence is the Robinson-Schensted-Knuth algorithm (or RSK) which gives a one-to-one correspondence between these pairs of Young tableaux and permutations. It can be described in various different ways. The equivalence of these different constructions are fascinating. The famous computer scientist Donald Knuth said in 1972 "The unusual nature of these coincidences might lead us to suspect that some sort of witchcraft is operating behind the scene". This talk, accessible to every one, illustrates the nowadays style of combinatorial mathematics: visual, concrete, related to deep mathematics and magic.