Spanning Trees on the Two-Dimensional Lattices with More Than One Type of Vertex (2008)
For a two-dimensional lattice $\Lambda$ with $n$ vertices, the number of spanning trees $N_{ST}(\Lambda)$ grows asymptotically as $\exp(n z_\Lambda)$ in the thermodynamic limit. We present exact...
Number of connected spanning subgraphs on the Sierpinski gasket (2008)
Chang, Shu-Chiuan, Chen, Lung-Chi
We study the number of connected spanning subgraphs $f_{d,b}(n)$ on the generalized Sierpinski gasket $SG_{d,b}(n)$ at stage $n$ with dimension $d$ equal to two, three and four for $b=2$, and layer...
Structure of spanning trees on the two-dimensional Sierpinski gasket (2008)
Chang, Shu-Chiuan, Chen, Lung-Chi
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...
Dimer coverings on the Sierpinski gasket with possible vacancies on the outmost vertices (2007)
Chang, Shu-Chiuan, Chen, Lung-Chi
We present the number of dimers $N_d(n)$ on the Sierpinski gasket $SG_d(n)$ at stage $n$ with dimension $d$ equal to two, three, four or five, where one of the outmost vertices is not covered when...
Exact Potts Model Partition Functions for Strips of the Honeycomb Lattice (2007)
Chang, Shu-Chiuan, Shrock, Robert
We present exact calculations of the Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature-like variable $v$ on $n$-vertex strip graphs $G$ of the honeycomb lattice for a...
Dimer-monomer model on the Sierpinski gasket (2007)
Chang, Shu-Chiuan, Chen, Lung-Chi
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...
Spanning forests on the Sierpinski gasket (2006)
Chang, Shu-Chiuan, Chen, Lung-Chi
We present the numbers of spanning forests 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...
Spanning trees on the Sierpinski gasket (2006)
Chang, Shu-Chiuan, Chen, Lung-Chi
We obtain the numbers of spanning trees on the Sierpinski gasket $SG_d(n)$ with dimension $d$ equal to two, three and four. The general expression for the number of spanning trees on $SG_d(n)$ with...
Spanning Trees on Lattices and Integration Identities (2006)
Chang, Shu-Chiuan, Wang, Wenya
For a lattice $\Lambda$ with $n$ vertices and dimension $d$ equal or higher than two, the number of spanning trees $N_{ST}(\Lambda)$ grows asymptotically as $\exp(n z_\Lambda)$ in the thermodynamic...
Some Exact Results for Spanning Trees on Lattices (2006)
Chang, Shu-Chiuan, Shrock, Robert
For $n$-vertex, $d$-dimensional lattices $\Lambda$ with $d \ge 2$, the number of spanning trees $N_{ST}(\Lambda)$ grows asymptotically as $\exp(n z_\Lambda)$ in the thermodynamic limit. We present an...
Chang, Shu-Chiuan, Shrock, Robert
We calculate the partition function $Z(G,Q,v)$ of the $Q$-state Potts model exactly for strips of the square and triangular lattices of various widths $L_y$ and arbitrarily great lengths $L_x$, with...
Chang, Shu-Chiuan, Shrock, Robert
We calculate the partition function $Z(G,Q,v)$ of the $Q$-state Potts model exactly for self-dual cyclic square-lattice strips of various widths $L_y$ and arbitrarily great lengths $L_x$, with $Q$...
Zeros of the Potts Model Partition Function in the Large-$q$ Limit (2005)
Chang, Shu-Chiuan, Shrock, Robert
We study the zeros of the $q$-state Potts model partition function $Z(\Lambda,q,v)$ for large $q$, where $v$ is the temperature variable and $\Lambda$ is a section of a regular $d$-dimensional...
Transfer Matrices for the Partition Function of the Potts Model on Toroidal Lattice Strips (2005)
Chang, Shu-Chiuan, Shrock, Robert
We present a method for calculating transfer matrices for the $q$-state Potts model partition functions $Z(G,q,v)$, for arbitrary $q$ and temperature variable $v$, on strip graphs $G$ of the square...
Exact Potts Model Partition Functions for Strips of the Triangular Lattice (2005)
Chang, Shu-Chiuan, Jacobsen, Jesper-Lykke, Salas, Jesus, Shrock, Robert
We present exact calculations of the Potts model partition function Z(G,q,v) for arbitrary q and temperature-like variable v on n-vertex strip graphs G of the triangular lattice for a variety of...
Exact Results for Average Cluster Numbers in Bond Percolation on Lattice Strips (2004)
Chang, Shu-Chiuan, Shrock, Robert
We present exact calculations of the average number of connected clusters per site, $$, as a function of bond occupation probability $p$, for the bond percolation problem on infinite-length strips of...
Chang, Shu-Chiuan, Shrock, Robert
We present a method for calculating transfer matrices for the $q$-state Potts model partition functions $Z(G,q,v)$, for arbitrary $q$ and temperature variable $v$, on cyclic and M\"obius strip graphs...
Chang, Shu-Chiuan, Shrock, Robert
We present transfer matrices for the zero-temperature partition function of the $q$-state Potts antiferromagnet (equivalently, the chromatic polynomial) on cyclic and M\"obius strips of the square,...
Exact Potts Model Partition Functions for Strips of the Triangular Lattice (2004)
Chang, Shu-Chiuan, Jacobsen, Jesper-Lykke, Salas, Jesus, Shrock, Robert
We present exact calculations of the Potts model partition function Z(G,q,v) for arbitrary q and temperature-like variable v on n-vertex strip graphs G of the triangular lattice for a variety of...
Exact Potts Model Partition Functions for Strips of the Triangular Lattice (2004)
Chang, Shu-Chiuan, Jacobsen, Jesper-Lykke, Salas, Jesus, Shrock, Robert
We present exact calculations of the Potts model partition function Z(G,q,v) for arbitrary q and temperature-like variable v on n-vertex strip graphs G of the triangular lattice for a variety of...
Some Exact Formulas on Long-Range Correlation Functions of the Rectangular Ising Lattice (2003)
Chang, Shu-Chiuan, Suzuki, Masuo
We study long-range correlation functions of the rectangular Ising lattice with cyclic boundary conditions. Specifically, we consider the situation in which two spins are on the same column, and at...
Exact Potts Model Partition Functions for Strips of the Triangular Lattice (2002)
Chang, Shu-Chiuan, Jacobsen, Jesper Lykke, Salas, Jesús, Shrock, Robert
We present exact calculations of the Potts model partition function Z(G,q,v) for arbitrary q and temperature-like variable v on n-vertex strip graphs G of the triangular lattice for a variety of...
Reliability Polynomials and their Asymptotic Limits for Families of Graphs (2002)
Chang, Shu-Chiuan, Shrock, Robert
We present exact calculations of reliability polynomials $R(G,p)$ for lattice strips $G$ of fixed widths $L_y \le 4$ and arbitrarily great length $L_x$ with various boundary conditions. We introduce...
Flow Polynomials and their Asymptotic Limits for Lattice Strip Graphs (2002)
Chang, Shu-Chiuan, Shrock, Robert
We present exact calculations of flow polynomials $F(G,q)$ for lattice strips of various fixed widths $L_y$ and arbitrarily great lengths $L_x$, with several different boundary conditions. Square,...
General Structural Results for Potts Model Partition Functions on Lattice Strips (2002)
Chang, Shu-Chiuan, Shrock, Robert
We present a set of general results on structural features of the $q$-state Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature Boltzmann variable $v$ for various lattice...
Exact results on q-state Potts model partition functions / (2002)
Thesis (Ph. D.)--State University of New York at Stony Brook, 2002.
Tutte Polynomials and Related Asymptotic Limiting Functions for Recursive Families of Graphs (2001)
Chang, Shu-Chiuan, Shrock, Robert
We prove several theorems concerning Tutte polynomials $T(G,x,y)$ for recursive families of graphs. In addition to its interest in mathematics, the Tutte polynomial is equivalent to an important...
Exact Chromatic Polynomials for Toroidal Chains of Complete Graphs (2001)
We present exact calculations of the partition function of the zero-temperature Potts antiferromagnet (equivalently, the chromatic polynomial) for graphs of arbitrarily great length composed of...
Exact Potts Model Partition Function for Strips of the Square Lattice (2001)
Salas, Jesus, Chang, Shu-Chiuan, Shrock, Robert
We present exact calculations of the Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature-like variable $v$ on $n$-vertex square-lattice strip graphs $G$ for a variety of...
Chang, Shu-Chiuan, Shrock, Robert
We present exact calculations of the Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature-like variable $v$ on self-dual strip graphs $G$ of the square lattice with fixed width...
Potts Model Partition Functions for Self-Dual Families of Strip Graphs (2001)
Chang, Shu-Chiuan, Shrock, Robert
We consider the $q$-state Potts model on families of self-dual strip graphs $G_D$ of the square lattice of width $L_y$ and arbitrarily great length $L_x$, with periodic longitudinal boundary...
Zeros of Jones Polynomials for Families of Knots and Links (2001)
Chang, Shu-Chiuan, Shrock, Robert
We calculate Jones polynomials $V_L(t)$ for several families of alternating knots and links by computing the Tutte polynomials $T(G,x,y)$ for the associated graphs $G$ and then obtaining $V_L(t)$ as...
Upper Bound for the Coefficients of Chromatic polynomials (2001)
This paper describes an improvement in the upper bound for the magnitude of a coefficient of a term in the chromatic polynomial of a general graph. If $a_r$ is the coefficient of the $q^r$ term in...
Exact Potts Model Partition Functions on Wider Arbitrary-Length Strips of the Square Lattice (2000)
Chang, Shu-Chiuan, Shrock, Robert
We present exact calculations of the partition function of the q-state Potts model for general q and temperature on strips of the square lattice of width L_y=3 vertices and arbitrary length L_x with...
Chromatic Polynomials for Lattice Strips with Cyclic Boundary Conditions (2000)
The zero-temperature $q$-state Potts model partition function for a lattice strip of fixed width $L_y$ and arbitrary length $L_x$ has the form...
Exact Potts Model Partition Functions on Strips of the Honeycomb Lattice (2000)
Chang, Shu-Chiuan, Shrock, Robert
We present exact calculations of the partition function of the $q$-state Potts model on (i) open, (ii) cyclic, and (iii) M\"obius strips of the honeycomb (brick) lattice of width $L_y=2$ and...
Chang, Shu-Chiuan, Shrock, Robert
We present exact calculations of partition function $Z$ of the $q$-state Potts model with next-nearest-neighbor spin-spin couplings, both for the ferromagnetic and antiferromagnetic case, for...
Chang, Shu-Chiuan, Shrock, Robert
partial abstract: The $q$-state Potts model partition function (equivalent to the Tutte polynomial) for a lattice strip of fixed width $L_y$ and arbitrary length $L_x$ has the form...
Chang, Shu-Chiuan, Shrock, Robert
We present exact calculations of the zero-temperature partition function (chromatic polynomial) and $W(q)$, the exponent of the ground-state entropy, for the $q$-state Potts antiferromagnet with...
Exact Potts Model Partition Function on Strips of the Triangular Lattice (2000)
Chang, Shu-Chiuan, Shrock, Robert
In this paper we present exact calculations of the partition function $Z$ of the $q$-state Potts model and its generalization to real $q$, for arbitrary temperature on $n$-vertex strip graphs, of...
Ground State Entropy of the Potts Antiferromagnet on Strips of the Square Lattice (2000)
Chang, Shu-Chiuan, Shrock, Robert
We present exact solutions for the zero-temperature partition function (chromatic polynomial $P$) and the ground state degeneracy per site $W$ (= exponent of the ground-state entropy) for the...
Ground State Entropy of the Potts Antiferromagnet on Triangular Lattice Strips (2000)
Chang, Shu-Chiuan, Shrock, Robert
We present exact calculations of the zero-temperature partition function (chromatic polynomial) $P$ for the $q$-state Potts antiferromagnet on triangular lattice strips of arbitrarily great length...