Corpus ID: 222177810

Poincar\'e polynomial for fully commutative elements in the symmetric group

@article{Harbat2020PoincarePF,
  title={Poincar\'e polynomial for fully commutative elements in the symmetric group},
  author={Sadek Al Harbat and C. Blondel},
  journal={arXiv: Combinatorics},
  year={2020}
}
Let $W^c(A_n)$ be the set of fully commutative elements of the Coxeter group $W(A_n)$. Let $$ a_n(q)= \sum_{w \in W^c(A_n)} q^{l(w)} . $$ We compute $a_n(q)$. 

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