We extend the usual notion of fully commutative elements from the finite Coxeter groups to the complex reflection groups. We decompose the sets of fully commutative elements into natural subsets according to their combinatorial properties, and investigate the structure of these decompositions. As a consequence, we enumerate and describe the form of these elements for the complex reflection groups.
Bibliographical noteFunding Information:
This work was partially supported by a grant from the Simons Foundation (#318706).This work was partially supported by the National Research Foundation of Korea (NRF-2016R1C1B2013135).
© 2019 Elsevier Inc.
- Catalan Triangle
- Catalan numbers
- Complex reflection groups
- Fully commutative elements