The enumeration of fully commutative affine permutations

@article{Hanusa2010TheEO,
  title={The enumeration of fully commutative affine permutations},
  author={Christopher R. H. Hanusa and Brant C. Jones},
  journal={Eur. J. Comb.},
  year={2010},
  volume={31},
  pages={1342-1359}
}

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References

SHOWING 1-10 OF 43 REFERENCES

The Enumeration of Fully Commutative Elements of Coxeter Groups

A Coxeter group element w is fully commutative if any reduced expression for w can be obtained from any other via the interchange of commuting generators. For example, in the symmetric group of

Fully commutative elements and Kazhdan-Lusztig cells in the finite and affine coxeter groups

The main goal of the paper is to show that the fully commutative elements in the affine Coxeter group C n form a union of two-sided cells. Then we completely answer the question of when the fully

On the Fully Commutative Elements of Coxeter Groups

Let W be a Coxeter group. We define an element w ∈ W to be fully commutative if any reduced expression for w can be obtained from any other by means of braid relations that only involve commuting

Nilpotent Orbits and Commutative Elements

Abstract Let W be a simply laced Coxeter group with generating set S , and let W c denote the subset consisting of those elements whose reduced expressions have no substrings of the form sts for any

Generalized Jones traces and Kazhdan–Lusztig bases

Fully commutative Kazhdan-Lusztig cells

We investigate the compatibility of the set of fully commutative elements of a Coxeter group with the various types of Kazhdan-Lusztig cells using a canonical basis for a generalized version of the

Schubert varieties and short braidedness

LetW be a finite Weyl group. We give a characterization of those elements ofW whose reduced expressions avoid substrings of the formsts wheres andt are noncommuting generators. We give as an

On 321-Avoiding Permutations in Affine Weyl Groups

We introduce the notion of 321-avoiding permutations in the affine Weyl group W of type An − 1 by considering the group as a George group (in the sense of Eriksson and Eriksson). This enables us to

Freely braided elements in Coxeter groups, II

Combinatorics of Coxeter Groups

I.- The basics.- Bruhat order.- Weak order and reduced words.- Roots, games, and automata.- II.- Kazhdan-Lusztig and R-polynomials.- Kazhdan-Lusztig representations.- Enumeration.- Combinatorial