scholarly journals Spanning Trees on the Sierpinski Gasket

2007 ◽  
Vol 126 (3) ◽  
pp. 649-667 ◽  
Author(s):  
Shu-Chiuan Chang ◽  
Lung-Chi Chen ◽  
Wei-Shih Yang
Keyword(s):  
Spanning Trees ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket

scholarly journals Structure of spanning trees on the two-dimensional Sierpinski gasket

2011 ◽  
Vol Vol. 12 no. 3 (Combinatorics) ◽  
Author(s):  
Shu-Chiuan Chang ◽  
Lung-Chi Chen
Keyword(s):  
Probability Distribution ◽  
Spanning Tree ◽  
Spanning Trees ◽  
Sierpinski Gasket ◽  
Rational Numbers ◽  
Limiting Distribution ◽  
Two Dimensional ◽  
Sierpiński Gasket ◽  
Average Probability ◽  
International Audience

Combinatorics International audience Consider spanning trees on the two-dimensional Sierpinski gasket SG(n) where stage n is a non-negative integer. For any given vertex x of SG(n), we derive rigorously the probability distribution of the degree j ∈{1,2,3,4} at the vertex and its value in the infinite n limit. Adding up such probabilities of all the vertices divided by the number of vertices, we obtain the average probability distribution of the degree j. The corresponding limiting distribution φj gives the average probability that a vertex is connected by 1, 2, 3 or 4 bond(s) among all the spanning tree configurations. They are rational numbers given as φ1=10957/40464, φ2=6626035/13636368, φ3=2943139/13636368, φ4=124895/4545456.

scholarly journals Weighted Spanning Trees on some Self-Similar Graphs

10.37236/503 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Daniele D'Angeli ◽  
Alfredo Donno
Keyword(s):  
Generating Functions ◽  
Spanning Trees ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket ◽  
Finite Graphs ◽  
Sierpiński Graphs ◽  
Schreier Graphs ◽  
Finite Approximations ◽  
Self Similar ◽  
Ternary Tree

We compute the complexity of two infinite families of finite graphs: the Sierpiński graphs, which are finite approximations of the well-known Sierpiński gasket, and the Schreier graphs of the Hanoi Towers group $H^{(3)}$ acting on the rooted ternary tree. For both of them, we study the weighted generating functions of the spanning trees, associated with several natural labellings of the edge sets.

scholarly journals Dimer Coverings on the Sierpinski Gasket

2008 ◽  
Vol 131 (4) ◽  
pp. 631-650 ◽  
Author(s):  
Shu-Chiuan Chang ◽  
Lung-Chi Chen
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket

scholarly journals Metric approximations of spectral triples on the Sierpiński gasket and other fractal curves

2021 ◽  
Vol 385 ◽  
pp. 107771
Author(s):  
Therese-Marie Landry ◽  
Michel L. Lapidus ◽  
Frédéric Latrémolière
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket ◽  
Spectral Triples

scholarly journals Level sets of harmonic functions on the Sierpiński gasket

2002 ◽  
Vol 40 (2) ◽  
pp. 335-362 ◽  
Author(s):  
Anders Öberg ◽  
Robert S. Strichartz ◽  
Andrew Q. Yingst
Keyword(s):  
Level Sets ◽  
Harmonic Functions ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket

Design Sierpinski Gasket Antenna for WLAN Application

2007 ◽  
Author(s):  
C.Z.C. Ghani ◽  
M.H.A. Wahab ◽  
N. Abdullah ◽  
S.A Hamzah ◽  
A. Ubin ◽  
...  
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket

scholarly journals Gradients of Laplacian eigenfunctions on the Sierpinski gasket

2008 ◽  
Vol 137 (02) ◽  
pp. 531-540 ◽  
Author(s):  
Jessica L. DeGrado ◽  
Luke G. Rogers ◽  
Robert S. Strichartz
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket
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