Acyclic orientations on the Sierpinski gasket

TL;DR

This paper investigates the number and growth behavior of acyclic orientations on the Sierpinski gasket, providing asymptotic analysis and bounds for various dimensions and parameters.

Contribution

It offers the first detailed asymptotic analysis and bounds for acyclic orientations on the Sierpinski gasket across different dimensions and configurations.

Findings

Derived asymptotic behaviors for acyclic orientations on $SG_{2,b}(n)$.

Established upper bounds for growth constants of acyclic orientations.

Extended analysis to $d$-dimensional Sierpinski gaskets.

Abstract

We study the number of acyclic orientations on the generalized two-dimensional Sierpinski gasket $SG_{2,b}(n)$ 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 $SG_{2,b}$ and $d$-dimensional Sierpinski gasket $SG_d$.