scholarly journals Diameters of graphs of reduced words and rank-two root subsystems

2021 ◽  
Author(s):  
Christian Gaetz ◽  
Yibo Gao
Keyword(s):  
Reduced Words

scholarly journals DISCRETE SOLITONS IN INFINITE REDUCED WORDS

2018 ◽  
Vol 24 (1) ◽  
pp. 31-66
Author(s):  
MAX GLICK ◽  
PAVLO PYLYAVSKYY
Keyword(s):  
Discrete Solitons ◽  
Reduced Words

Basics

2018 ◽  
pp. 7-8
Author(s):  
Christophe Reutenauer
Keyword(s):  
Free Group ◽  
Free Groups ◽  
Free Monoid ◽  
Periodic Pattern ◽  
Infinite Words ◽  
Reduced Words

Definitions and basic results about words: alphabet, length, free monoid, concatenation, prefix, suffix, factor, conjugation, reversal, palindrome, commutative image, periodicity, ultimate periodicity, periodic pattern, infinite words, bi-infinite words, free groups, reduced words, homomorphisms, embedding of a free monoid in a free group, abelianization,matrix of an endomorphism, GL2(Z), SL2(Z).

A remark about the description of free products of groups

1966 ◽  
Vol 62 (2) ◽  
pp. 129-134 ◽  
Author(s):  
John Stallengs
Keyword(s):  
Free Product ◽  
Binary Operation ◽  
Free Products ◽  
Products Of Groups ◽  
Reduced Words

The free product A* B of groups A and B can be described in two ways.We can construct the set of reduced words in A and B. Define a binary operation on by concatenating two words and performing as many reductions as possible. Prove that is a group; the difficult step is the proof of associativity. Define A * B = .

scholarly journals Diameter of graphs of reduced words and galleries

2012 ◽  
Vol 365 (5) ◽  
pp. 2779-2802 ◽  
Author(s):  
Victor Reiner ◽  
Yuval Roichman
Keyword(s):  
Reduced Words

scholarly journals Tableaux on k+1-cores, reduced words for affine permutations, and k-Schur expansions

2005 ◽  
Vol 112 (1) ◽  
pp. 44-81 ◽  
Author(s):  
Luc Lapointe ◽  
Jennifer Morse
Keyword(s):  
Affine Permutations ◽  
Reduced Words

scholarly journals Intervals and factors in the Bruhat order

2015 ◽  
Vol Vol. 17 no. 1 (Combinatorics) ◽  
Author(s):  
Bridget Eileen Tenner
Keyword(s):  
Symmetric Group ◽  
Bruhat Order ◽  
Order Ideal ◽  
Principal Order ◽  
International Audience ◽  
Reduced Words

Combinatorics International audience In this paper we study those generic intervals in the Bruhat order of the symmetric group that are isomorphic to the principal order ideal of a permutation w, and consider when the minimum and maximum elements of those intervals are related by a certain property of their reduced words. We show that the property does not hold when w is a decomposable permutation, and that the property always holds when w is the longest permutation.

scholarly journals Cyclic Sieving for Longest Reduced Words in the Hyperoctahedral Group

10.37236/339 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
T. Kyle Petersen ◽  
Luis Serrano
Keyword(s):  
Generating Function ◽  
Hyperoctahedral Group ◽  
Cyclic Action ◽  
Orbit Structure ◽  
Cyclic Sieving Phenomenon ◽  
Major Index ◽  
Cyclic Sieving ◽  
Reduced Words

We show that the set $R(w_0)$ of reduced expressions for the longest element in the hyperoctahedral group exhibits the cyclic sieving phenomenon. More specifically, $R(w_0)$ possesses a natural cyclic action given by moving the first letter of a word to the end, and we show that the orbit structure of this action is encoded by the generating function for the major index on $R(w_0)$.

scholarly journals Infinite reduced words, lattice property and braid graph of affine Weyl groups

2019 ◽  
Vol 536 ◽  
pp. 170-214 ◽  
Author(s):  
Weijia Wang
Keyword(s):  
Weyl Groups ◽  
Affine Weyl Groups ◽  
Lattice Property ◽  
Reduced Words
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