Consecutive patterns in Coxeter groups

For an arbitrary Coxeter group element a and a connected subset J of the Dynkin diagram, the parabolic decomposition a = aJaJ defines aJ as a consecutive pattern of a, gener-alizing the notion of consecutive patterns in permutations. We then define the cc-Wilf-equivalence classes as an exten-sion of the c-Wilf-equivalence classes for permutations, and identify non-trivial families of cc-Wilf-equivalent classes. Fur-thermore, we study the structure of the consecutive pattern poset in Coxeter groups and prove that its Mobius function is bounded by 2 when the arguments belong to finite Coxeter groups, but can be arbitrarily large otherwise. & COPY; 2023 Elsevier Inc. All rights reserved.