$S_n$ as a Coxeter group? (with Matsumoto's theorem)

Question

I need to find a book in which basic $S_n$ theory is covered, mainly the part about Bruhat order, length of an element $w \in S_n$ and invariance modulo braid relations of the expressions $w=s_{i_1}\dots s_{i_k}$ (Matsumoto's theorem)

Are you aware of any good reference?

Answer 1

I can't say I've heard it called Matsumoto's theorem, but there are quite a few references having this information. A classic is Reflection Groups and Coxeter Groups by Humphreys, and a more recent one is Combinatorics of Coxeter groups by Bjorner and Brenti, which has quite a bit about $S_n$ (though most of the book works in a more general setting).