A complex hyperbolic triangle group is the group of complex hyperbolic isometries generated by complex involutions fixing three complex lines in complex hyperbolic space. Such a group is called equilateral if there is an isometry of order three that cyclically permutes the three complex lines. We consider equilateral triangle groups for which the product of each pair of involutions and the prod...

Let K be a field and P partially ordered set (poset). FI(P,K) I(P,K) the finitary incidence algebra space of over K, respectively, let D(P,K)=FI(P,K)⊕I(P,K) idealization FI(P,K)-bimodule I(P,K). In first part this paper, we show that D(P,K) has an anti-automorphism (involution) if only (involution). We also present characterization anti-automorphisms involutions on D(P,K). second part, obtain c...

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.

We study the sublattices of the rank 2d Barnes-Wall lattices BW2d which occur as fixed points of involutions. They have ranks 2d−1 (for dirty involutions) or 2d−1 ± 2k−1 (for clean involutions), where k, the defect, is an integer at most d2 . We discuss the involutions on BW2d and determine the isometry groups of the fixed point sublattices for all involutions of defect 1. Transitivity results ...

Centrosymmetric involutions in the symmetric group S2n are permutations π such that π = π−1 and π(i) + π(2n + 1 − i) = 2n + 1 for all i, and they are in bijection with involutions of the hyperoctahedral group. We describe the distribution of some natural descent statistics on 321-avoiding centrosymmetric involutions, including the number of descents in the first half of the involution, and the ...

Centrosymmetric involutions in the symmetric group S2n are permutations π such that π = π−1 and π(i) + π(2n+1− i) = 2n+1 for all i, and they are in bijection with involutions of the hyperoctahedral group. We describe the distribution of some natural descent statistics on 321-avoiding centrosymmetric involutions, including the number of descents in the first half of the involution, and the sum o...

Introduction. In a recent paper [l] attention was called to a new family of line involutions in 53 furnishing examples of involutions of all orders, m, ^4 with complexes of invariant lines of all possible orders, i, from 2 up to the maximum, [(»i + l)/2]. Since involutions of all orders without a complex of invariant lines are known to exist, and since examples of all possible involutions of or...

We present an extensive study of the Eulerian distribution on the set of centrosymmetric involutions, namely, involutions in Sn satisfying the property σ(i) + σ(n+ 1− i) = n+ 1 for every i = 1 . . . n. We find some combinatorial properties for the generating polynomial of such distribution, together with an explicit formula for its coefficients. Afterwards, we carry out an analogous study for t...