We present a library of formalized results around symmetric functions and the character theory of the symmetric groups. Written in Coq/Rocq and based on the Mathematical component library, it covers a large part of the contents of a basic textbook in the field. The central result is a proof of the Littlewood-Richardson rule, which computes some integer numbers appearing in various fields of mathematics, and which has a long story of wrong proofs. A specific feature of algebraic combinatorics is the constant interplay between algorithms and algebraic constructions: algorithms are not only in computations, but also are key ingredients in definitions and proofs. As such, the proof of the Littlewood-Richardson rule deeply relies on the understanding of the execution of the Robinson-Schensted algorithm. Many results in this library are effective and actually used in computer algebra systems, and we discuss their certified implementation.