Combinatorics of centers of 0-Hecke algebras in type \(A\) (Q6133157)

The author considers the symmetric group \(\mathrm{S}_n\). Building on work of \textit{M. Geck} et al. [J. Algebra 229, No. 2, 570--600 (2000; Zbl 1042.20026)], he obtains a complete set of representatives of the equivalence classes. This set is naturally parametrized by certain compositions of \(n\) called maximal. The author develops an explicit combinatorial description for the equivalence classes that are parametrized by the maximal compositions whose odd parts form a hook.