Acyclic orientations on the Sierpinski gasket

Abstract

We study the number of acyclic orientations on the generalized two-dimensional Sierpinski gasket $S{G}_{2,b}(n)$ at stage $n$ with $b$ equal to two and three, and determine the asymptotic behaviors. We also derive upper bounds for the asymptotic growth constants for $S{G}_{2,b}$ and $d$-dimensional Sierpinski gasket $S{G}_d$.

20 pages, 8 figures and 6 tables

References in corpus (4)

• Spanning trees on the Sierpinski gasket
• Dimer coverings on the Sierpinski gasket with possible vacancies on the outmost vertices
• Dimer-monomer model on the Sierpinski gasket
• Branched Polymers on the Given-Mandelbrot family of fractals

Cited by in corpus (3)

• Asymptotic Behavior of Acyclic and Cyclic Orientations of Directed Lattice Graphs
• Ice model and eight-vertex model on the two-dimensional Sierpinski gasket
• Potts Partition Function Zeros and Ground State Entropy on Hanoi Graphs