Joint spectrum and the infinite dihedral group

Non-commutative convolutional codes over the infinite dihedral group

Classic convolutional codes are defined as the convolution of a message and a transfer function over Z. In this paper, we study convolutional codes over the infinite dihedral group D∞. The goal of this study is to design convolutional codes with good and interesting properties and intended to be more resistant to code recognition. Convolution of two functions on D∞ corresponds to the product of...

Algebraic K-theory over the infinite dihedral group: a controlled topology approach

We use controlled topology applied to the action of the infinite dihedral group on a partially compactified plane and deduce two consequences for algebraic K-theory. The first is that the family in the K-theoretic Farrell–Jones conjecture can be reduced to only those virtually cyclic groups that admit a surjection with finite kernel onto a cyclic group. The second is that the Waldhausen Nil gro...

Symmetry classes of polynomials associated with the dihedral group

‎In this paper‎, ‎we obtain the dimensions of symmetry classes of polynomials associated with‎ ‎the irreducible characters of the dihedral group as a subgroup of‎ ‎the full symmetric group‎. ‎Then we discuss the existence of o-basis‎ ‎of these classes‎.

The Cofinality Spectrum of the Infinite Symmetric Group

Darboux transformation with Dihedral reduction group

We construct the Darboux transformation with Dihedral reduction group for the 2–dimensional generalisation of the periodic Volterra lattice. The resulting Bäcklund transformation can be viewed as a nonevolutionary integrable differential difference equation. We also find its generalised symmetry and the Lax representation for this symmetry. Using formal diagonalisation of the Darboux matrix we ...