7Permutations and the Rest. Algebraic Combinatorics of Permutations.
7.1 Robinson–Schensted–Knuth Correspondence
This chapter is devoted to the connections between permutations and various other objects in combinatorics. This is certainly a huge topic, and we can therefore only skim the surface of a few selected areas. Our goal is to give the reader an overview of some main lines of research to aid the decision of what literature to consult next.
In the first section, we present the famous Robinson–Schensted–Knuth correspondence that connects the combinatorics of permutations and the combinatorics of Standard Young Tableaux. There are several excellent books [185, 279], devoted entirely or mostly to the fascinating ...
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