The centralizer of a set of words X is the largest set of words C(X) commuting with X: XC(X) = C(X)X. It has been a long standing open question due to Conway, 1971, whether the centralizer of any rational set is rational. While the answer turned out to be negative in general, see Kunc 2004, we prove here that the situation is different for codes: the centralizer of any rational code is rational...

BACKGROUND AND PURPOSE A proximal stem centralizer may be beneficial regarding cementing pressures, cement penetration, and stem alignment. We measured these parameters when cementing a mat-surfaced femoral component with and without the use of a proximal stem centralizer. MATERIAL AND METHODS 8 femoral prostheses with proximal centralizers and 8 femoral prostheses without proximal centralize...

The normalizer of an element of a group is defined as the subgroup of all elements commuting with it; this subgroup is often also called the centralizer of the given element. In the second version [F-GM] the authors switched to the latter terminology, and we will also use the term “centralizer”. The conjecture was supported by a new algorithm for finding generators of a centralizer, suggested i...

In this paper, we establish Schur-Weyl reciprocity for the q-analogue of the alternating group. We analyze the sign q-permutation representation of the Hecke algebra HQ(q),r(q) on the rth tensor product of Z2-graded Q-vector space V = V0⊗V1 in detail, and examine its restriction to the qanalogue of the alternating group H1Q(q),r(q). In consequence, we find out that if dimV0 = dimV1, then the ce...

This paper gives necessary and sufficient conditions for the centralizer of a finite subgroup of outer automorphisms (resp. automorphisms) of a finitely generated free group to be finite. If G is realized by its action on a graph, Krstić’s work produces generators of the centralizer of G in terms of graph isomorphisms and certain graph transformations. This paper examines the behavior of these ...

On the torus of dimension 2, 3, or 4, we show that the subset of diffeomorphisms with trivial centralizer in the C topology has nonempty interior. We do this by developing two approaches, the fixed point and the odd prime periodic point, to obtain trivial centralizer for an open neighbourhood of Anosov diffeomorphisms arbitrarily near certain irreducible hyperbolic toral automorphism.

We give a new proof of Brink’s theorem that the nonreflection part of a reflection centralizer in a Coxeter group is free, and make several refinements. In particular we give an explicit finite set of generators for the centralizer and a method for computing the Coxeter diagram for its reflection part. In many cases, our method allows one to compute centralizers quickly in one’s head. We also d...