Related papers: Flag weak order on wreath products

The group property FW stands in-between the celebrated Kazdhan's property (T) and Serre's property FA. Among many characterizations, it might be defined, for finitely generated groups, as having all Schreier graphs one-ended. It follows…

Let $F$ be a field, let $V$ be a valuation ring of $F$ of arbitrary Krull dimension (rank), let $K$ be a finite Galois extension of $F$ with group $G$, and let $S$ be the integral closure of $V$ in $K$. Let $f:G\times G\mapsto K\setminus…

We describe an effective version of the conjugacy problem and study it for wreath products and free solvable groups. The problem involves estimating the length of short conjugators between two elements of the group, a notion which leads to…

Let $K$ be field of characteristic 2 and let $G$ be a finite non-abelian 2-group with the cyclic derived subgroup $G'$, and there exists a central element $z$ of order 2 in $Z(G) \backslash G'$. We prove that the unit group of the group…

For an $n$-tuple $s$ of non-negative integers, the $s$-weak order is a lattice structure on $s$-trees, generalizing the weak order on permutations. We first describe the join irreducible elements, the canonical join representations, and the…

Given sofic approximations for countable, discrete groups $G,H$, we construct a sofic approximation for their wreath product $G\wr H$.

We exhibit exponentially distorted subgroups in $\mathbb{Z} \wr ( \mathbb{Z} \wr \mathbb{Z} )$ and $\mathbb{Z} \wr F_2$.

The W-set of an element of a weak order poset is useful in the cohomological study of the closures of spherical subgroups in generalized flag varieties. We explicitly describe in a purely combinatorial manner the W-sets of the weak order…

Given a sequence of $(G_i)_{i \in \N}$ of finite transitive groups of degree $n_i$, let $W_\infty$ be the inverse limit of the iterated permutational wreath products of the first m groups. We prove that $W_\infty$ is (topologically)…

Motivated by the study of pattern avoidance in the context of permutations and ordered partitions, we consider the enumeration of weak-ordering chains obtained as leaves of certain restricted rooted trees. A tree of order $n$ is generated…

A permutation class which is closed under pattern involvement may be described in terms of its basis. The wreath product construction X \wr Y of two permutation classes X and Y is also closed, and we investigate classes Y with the property…

In this paper we consider arbitrary intervals in the left weak order on the symmetric group $S_n$. We show that the Lehmer codes of permutations in an interval form a distributive lattice under the product order. Furthermore, the…

We investigate a semigroup construction related to the two-sided wreath product. It encompasses a range of known constructions and gives a slightly finer version of the decomposition in the Krohn-Rhodes Theorem, in which the three-element…

We construct a poset from a simple acyclic digraph together with a valuation on its vertices, and we compute the values of its M\"obius function. We show that the weak order on Coxeter groups of type A, B, affine A, and the flag weak order…

In "Hopf algebra of the planar binary trees", Adv. Math. 139 (1998), no. 2, 293--309, we constructed by induction a graded associative product on the vector space generated by the planar binary trees (resp. the permutations). In the present…

We present several multi-variable generating functions for a new pattern matching condition on the wreath product of the cyclic group and the symmetric group. Our new pattern matching condition requires that the underlying permutations…

Wreath products involving symmetric inverse monoids/semigroups/categories arise in many areas of algebra and science, and presentations by generators and relations are crucial tools in such studies. The current paper finds such…

We show that if $G$ and $H$ are finitely generated groups whose Hilbert compression exponent is positive, then so is the Hilbert compression exponent of the wreath $G \wr H$. We also prove an analogous result for coarse embeddings of wreath…

We completely characterize the logical hierarchy of various subsystems of weak arithmetic, namely: ZR, ZR + N, ZR + GCD, ZR + Bez, OI + N, OI + GCD, OI + Bez.

Let I be a finite partially ordered set and let (Sym({\Delta}i),{\Delta}i)i be a sequence of symmetric groups indexed by I. Construct the generalised wreath product (F, {\Delta}) on this sequence of permutation groups. We determine the…