## 31 Citations

### Chapter 1 Affine Permutations and an Affine Coxeter Monoid

- Mathematics
- 2013

In this expository paper, we describe results on pattern avoidance arising from the affine Catalan monoid. The schema of affine codes as canonical decompositions in conjunction with two-row moves is…

### Affine Permutations and an Affine Catalan Monoid

- Mathematics
- 2014

We describe results on pattern avoidance arising from the affine Catalan monoid. The schema of affine codes as canonical decompositions in conjunction with two-row moves is detailed, and then applied…

### Length enumeration of fully commutative elements in finite and affine Coxeter groups

- MathematicsJournal of Algebra
- 2018

### Rational generating series for affine permutation pattern avoidance

- Mathematics
- 2015

We consider the set of affine permutations that avoid a fixed permutation pattern. Crites has given a simple characterization for when this set is infinite. We find the generating series for this set…

### Combinatorics of fully commutative involutions in classical Coxeter groups

- MathematicsDiscret. Math.
- 2015

### 321-avoiding Affine Permutations, Heaps, and Periodic Parallelogram Polyominoes

- MathematicsElectron. Notes Discret. Math.
- 2017

### Long Fully Commutative Elements in Affine Coxeter Groups

- MathematicsIntegers
- 2015

It is proved among other things that, for each irreducible affine Coxeter group, the sequence counting fully commutative elements with respect to length is ultimately periodic.

### Fully commutative elements and lattice walks

- Mathematics
- 2013

An element of a Coxeter group W is fully commutative if any two of its reduced decompositions are related by a series of transpositions of adjacent commuting generators. These elements were…

### On the length of fully commutative elements

- Mathematics
- 2015

In a Coxeter group $W$, an element is fully commutative if any two of its reduced expressions can be linked by a series of commutation of adjacent letters. These elements have particularly nice…

### # A 36 INTEGERS 15 ( 2015 ) LONG FULLY COMMUTATIVE ELEMENTS IN AFFINE COXETER GROUPS

- Mathematics
- 2015

An element of a Coxeter group W is fully commutative if any two of its reduced decompositions are related by a series of transpositions of adjacent commuting generators. In the preprint Fully…

## References

SHOWING 1-10 OF 43 REFERENCES

### The Enumeration of Fully Commutative Elements of Coxeter Groups

- Mathematics
- 1998

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

- Mathematics
- 2003

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

- Mathematics
- 1996

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

- Mathematics
- 1997

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…

### Fully commutative Kazhdan-Lusztig cells

- Mathematics
- 2001

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

- Mathematics
- 1998

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

- Mathematics
- 2001

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…

### Combinatorics of Coxeter Groups

- Mathematics
- 2005

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…