On Inflation Rules for Mosseri-Sadoc Tilings

TL;DR

This paper derives inflation rules for decorated Mosseri-Sadoc tiles within a specific tiling class, linking Dehn invariants to eigenvectors of the inflation matrix associated with the golden ratio.

Contribution

It provides the inflation rules for decorated Mosseri-Sadoc tiles and connects Dehn invariants to the eigenstructure of the inflation matrix.

Findings

Eigenvalues of the inflation matrix are related to the golden ratio.

Dehn invariants serve as eigenvectors of the inflation matrix.

Explicit inflation rules for decorated Mosseri-Sadoc tiles are established.

Abstract

We give the inflation rules for the decorated Mosseri-Sadoc tiles in the projection class of tilings ${\cal T}^{(MS)}$. Dehn invariants related to the stone inflation of the Mosseri-Sadoc tiles provide eigenvectors of the inflation matrix with eigenvalues equal to $\tau = \frac{1+\sqrt{5}}{2}$ and $-\tau^{-1}$.