Dimer-monomer model on the Sierpinski gasket

TL;DR

This paper calculates the number of dimer-monomers on Sierpinski gaskets of various dimensions and scales, analyzing their asymptotic behaviors and extending results to generalized gaskets with different parameters.

Contribution

It provides exact counts and asymptotic analysis of dimer-monomers on Sierpinski gaskets and their generalizations, expanding understanding of combinatorial properties on fractal structures.

Findings

Number of dimer-monomers on $SG_d(n)$ for $d=2,3,4$

Asymptotic behaviors of these counts

Results for generalized Sierpinski gaskets $SG_{d,b}(n)$ with $b=3,4$

Abstract

We present the numbers of dimer-monomers on the Sierpinski gasket $SG_d(n)$ at stage $n$ with dimension $d$ equal to two, three and four, and determine the asymptotic behaviors. The corresponding results on the generalized Sierpinski gasket $SG_{d,b}(n)$ with $d=2$ and $b=3,4$ are obtained.