Irreducible subshifts associated with A2 buildings (2003)

Author(s): Robertson G; Steger T

    Abstract: Let $\Gamma$ be a group of type rotating automorphisms of a building $\cB$ of type $\widetilde A_2$, and suppose that $\Gamma$ acts freely and transitively on the vertex set of $\cB$. The apartments of $\cB$ are tiled by triangles, labelled according to $\Gamma$-orbits. Associated with these tilings there is a natural subshift of finite type, which is shown to be irreducible. The key element in the proof is a combinatorial result about finite projective planes.

      • Date: 19-06-2003
      • Journal: Journal of Combinatorial Theory, Series A
      • Volume: 103
      • Issue: 1
      • Pages: 91-104
      • Publisher: Academic Press
      • Publication type: Article
      • Bibliographic status: Published