[PDF] Top 20 Classes of maximal length reduced words in Coxeter groups

... Commutation Classes of Reduced Words 1.1 Finite Coxeter Groups and Root Systems We begin with a brief overview of basic Coxeter group theory, following [Humphreys].. No originality is cl[r] ... See full document

... Conjugacy classes of finite Coxeter groups have long been of interest, the cor- respondence between partitions and the conjugacy classes for the symmetric groups having been observed by ... See full document

... [finite] groups admit Beauville structures?” as well as the more difficult question of which Beauville groups are strongly real Beauville ...several classes of finite groups including abelian ... See full document

... For right cosets Xg and Xh of X we write Xg ∼ Xh whenever Xgt = Xh for some t ∈ Ref( W ) and Xg and Xh have the same Coxeter length. Let ≈ be the equivalence relation generated by ∼ on the set of right ... See full document

... This is true in the case of Coxeter groups. For example, Richardson [7] gives an e¤ective algorithm for parameterizing the involution conjugacy classes of a Coxeter group. In something of the ... See full document

... It follows tliat zoj = 0 for all j, and tliat amongst the entries ZiQ,yn,zn , ... , yir, Zir, tliere will be only one non-zero entry equal to pi. The set of templates Q (if any) that satisfy this fall into a number of ... See full document

... conjugacy classes are parameterised by signed cycle type, so that involutions are conjugate if and only if they have the same number, m, of transpositions (all of which must be positive), and the same number, e, ... See full document

... in Coxeter groups, and show how this relates to ordinary problems in reducibility and ...cyclic words, cyclic commutativity classes, as well as cyclically and torically reduced ... See full document

... minimal length in W -conjugacy classes, which gives as a byproduct (in Corollaries ...a Coxeter group W , we have that Φ is the disjoint union of the set of positive roots Φ + and the set of negative ... See full document

... Weyl groups, we have checked all conjugacy classes of these groups for n up to 10, and in each case every element of maximal length in a conjugacy class has excess ...of maximal ... See full document

... Coxeter groups. We manage to solve the problem for all finite classical Coxeter groups, and the quasiparabolic subgroups are listed in Theorem 16 of Chapter ... See full document

... crystallographic groups by two nodes and show that these do not induce any further affine ...non-crystallographic Coxeter groups from a recent paper and compare the induced extensions with the ... See full document

... We briefly describe the maximal period linear recurring sequences, a previously known family of words over f0; 1g; such words exist for every length of the form l = 2n 1 and their autodi[r] ... See full document

... On the other hand, taking into consideration the shape of the SSNs, Ticker et al. [34], in 1998, divid- ed them into two types, namely a U-type (U-shaped SSN 77%) and a V-type (V-shaped SSN 23%). The degree of ... See full document

... underlying class ˆ X in W . To determine the Coxeter graph corresponding to ˆ X, note that if I ⊆ W , then ˆ X has the same graph as X. If x = (a, u) is a product of k reflections in ˜ W , then a must be a product ... See full document

... groups. In section 3 we apply these notions to affine Toda field theory and construct in particular their classical mass spectra and fusing structures. In addition we start the de- velopment of a quantum field ... See full document

... are pairwise permutable, they all have interesting covering/avoidance properties and the given Sylow system reduces into each of them. As an example at the end of Chapter 4 shows, can be as large as the preceding ... See full document

... In this section we first give in Theorem 2.1 necessary conditions for U (Γ) to be finite. These will turn out also to be sufficient conditions. For each case not eliminated by Theorem 2.1 we then find an expression for U ... See full document

... infinite groups. It is for instance obvious that finitely generated F C-groups are finite over the centre, while an arbitrary F C -group G is residually finite over Z ... See full document

... S1nce every element has tinite order, as elements ot GLm,pn, then matrices of this torm give a subsroup c4 GLm,pn... The order of this subcroup 1s eas1ly seen.[r] ... See full document