The Number of Group Homomorphisms from D[subscript m] into D[subscript n].

@article{Johnson2013TheNO,
  title={The Number of Group Homomorphisms from D[subscript m] into D[subscript n].},
  author={Jeremiah W. Johnson},
  journal={College Mathematics Journal},
  year={2013},
  volume={44},
  pages={190-192}
}
Counting homomorphisms between cyclic groups is a common exercise in a first course in abstract algebra. A similar problem, accessible at the same level, is to count the number of group homomorphisms from a dihedral group of order $2m$ into a dihedral group of order $2n$. While the solution requires only elementary group theory, the result does not appear in the literature or in the usual texts. As the solution may be of interest, particularly to those teaching undergraduate abstract algebra… 

Symmetry and the Vector Allen–Cahn Equation: Crystalline and Other Complex Structures

We present a systematic study of entire symmetric solutions \(u:{\mathbb R}^n \to {\mathbb R}^m\) of the vector Allen–Cahn equation Δu − Wu(u) = 0, \(x \in {\mathbb R}^n\), where \(W:{\mathbb R}^m

Multiphase Solutions to the Vector Allen–Cahn Equation: Crystalline and Other Complex Symmetric Structures

AbstractWe present a systematic study of entire symmetric solutions $${u : \mathbb{R}^n \rightarrow\mathbb{R}^m}$$u:Rn→Rm of the vector Allen–Cahn equation $$\Delta u - W_u(u) = 0 \quad\text{for

Multiphase Solutions to the Vector Allen–Cahn Equation: Crystalline and Other Complex Symmetric Structures

We present a systematic study of entire symmetric solutions u:Rn→Rm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}