This book gives a unified introduction to the rapidly develo** area of finite tight frames.
Fifteen years ago, the existence of equal-norm tight frames of n> d vectors for Rd and Cd …

We determine the distribution of the sandpile group (or Jacobian) of the Erdős-Rényi
random graph $ G (n, q) $ as $ n $ goes to infinity. We prove the distribution converges to a …

Reversibility is a thread woven through many branches of mathematics. It arises in
dynamics, in systems that admit a time-reversal symmetry, and in group theory where the …

Let X be a finite dimensional compact metrizable space. We study a technique which
employs semiprojectivity as a tool to produce approximations of C (X)-algebras by C (X) …

Recently it was shown that there is a unique Z4R symmetry for the MSSM which allows for
the Yukawa couplings and dimension five neutrino mass operator, forbids the μ term and …

The main theorem of this paper is that if $(N,+) $ is a finite abelian $ p $-group of $ p $-rank
$ m $ where $ m+ 1< p $, then every regular abelian subgroup of the holomorph of $ N $ is …

Symmetries of three-dimensional topological field theories are naturally defined in terms of
invertible topological surface defects. Symmetry groups are thus Brauer–Picard groups. We …

Quantum channels, a subset of quantum maps, describe the unitary and nonunitary
evolution of quantum systems. We study a generalization of the concept of Pauli maps to the …

A subgroup H of a group G is said to be pronormal in G if each of its conjugates H g in G is
already conjugate to it in the subgroup⟨ H, H g⟩. Extending the well-known class of …

The isomorphism problem for finite groups of order n (GpI) has long been known to be
solvable in n^\logn+O(1) time, but only recently were polynomial-time algorithms designed …