Let W be a finite Coxeter group and X a subset of W . The length polynomial LW,X(t) is defined by LW,X(t) = ∑ x∈X t `(x), where ` is the length function on W . In this article we derive expressions for the length polynomial where X is any conjugacy class of involutions, or the set of all involutions, in any finite Coxeter group W . In particular, these results correct errors in [6] for the invo...

We study hamiltonian actions of compact groups in the presence of compatible involutions. We show that the lagrangian fixed point set on the symplectically reduced space is isomorphic to the disjoint union of the involutively reduced spaces corresponding to involutions on the group strongly inner to the given one. Our techniques imply that the solution to the eigenvalues of a sum problem for a ...

This paper studies the equivariant cobordism classification of all involutions fixing a disjoint union of an odd-dimensional real projective space RP with its normal bundle nonbounding and a Dold manifold P (h, i) with h > 0 and i > 0. For odd h, the complete analysis of the equivariant cobordism classes of such involutions is given except that the upper and lower bounds on codimension of P (h,...

In this paper, an explicit classification of smooth free involutions on S×S up to conjugation is obtained.

We give a simple combinatorial proof of three identities of Warnaar. The proofs exploit involutions due to Franklin and Schur.

Several recent works have explored the deep structure between arc diagrams, their nestings and crossings, and several other combinatorial objects including permutations, graphs, lattice paths, and walks in the Cartesian plane. This thesis inspects a range of related combinatorial objects that can be represented by arc diagrams, relationships between them, and their connection to nestings and cr...

We prove the parallelogram inequalities in metric spaces and use them to obtain the fixed points of involutions.

Let (W,6) be a finite Coxeter system, and θ an involution such that θ(1) = 1, where 1 is a basis for the root system 8 associated with W . We show that the set of θ-twisted involutions in W , Iθ = {w ∈ W | θ(w) = w−1} is in one to one correspondence with the set of regular involutions IId. The elements of Iθ are characterized by sequences in 6 which induce an ordering called the Bruhat Lattice....

We investigate the natural codings of linear involutions. We deduce from the geometric representation of linear involutions as Poincaré maps of measured foliations a suitable definition of return words which yields that the set of first return words to a given word is a symmetric basis of the free group on the underlying alphabet A. The set of first return words with respect to a subgroup of fi...

The aim of this note is to determine certain closed subgroups of the absolute Galois group G(Q) of Q, in particular subgroups generated by involutions (=elements of order 2). Geyer [3,4.1] has shown, in a far more general set-up, that subgroups generated by finitely many involutions are almost always free profinite products of copies of Z/22. To be precise, fix an involution E E G(Q); for almos...