Non-existence of phase transition of oriented percolation on Sierpinski carpet lattices

 A percolation problem on Sierpinski carpet lattices is considered. It is obtained that the critical probability \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} of oriented percolation is equal to 1. In contrast it was already shown that the critical probability pc of percolation is strictly less than 1 in Kumagai [9]. This result shows a difference between fractal-like lattice and ℤd lattice.