Arithmetic theory of brick tilings

A new, “arithmetic”, approach to the algebraic theory of brick tilings is developed. This approach enables one to construct a simple classification of brick tilings in ${\mathbb Z}^d$ and to find new proofs of several classical results on brick packing and tilings in ${\mathbb Z}^d$. In addition, possible generalizations of results on integer brick packing to the Euclidean plane $\mathbb R^2$ are investigated.