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enumeration of lattice paths and walks
 Date Issued:
 2011
 Summary:
 A wellknown long standing problem in combinatorics and statistical mechanics is to find the generating function for selfavoiding walks (SAW) on a twodimensional lattice, enumerated by perimeter. A SAW is a sequence of moves on a square lattice which does not visit the same point more than once. It has been considered by more than one hundred researchers in the pass one hundred years, including George Polya, Tony Guttmann, Laszlo Lovasz, Donald Knuth, Richard Stanley, Doron Zeilberger, Mireille BousquetMlou, Thomas Prellberg, Neal Madras, Gordon Slade, Agnes Dit tel, E.J. Janse van Rensburg, Harry Kesten, Stuart G. Whittington, Lincoln Chayes, Iwan Jensen, Arthur T. Benjamin, and many others. More than three hundred papers and a few volumes of books were published in this area. A SAW is interesting for simulations because its properties cannot be calculated analytically. Calculating the number of selfavoiding walks is a common computational problem. A recently proposed model called prudent selfavoiding walks (PSAW) was first introduced to the mathematics community in an unpublished manuscript of Pra, who called them exterior walks. A prudent walk is a connected path on square lattice such that, at each step, the extension of that step along its current trajectory will never intersect any previously occupied vertex. A lattice path composed of connected horizontal and vertical line segments, each passing between adjacent lattice points. We will discuss some enumerative problems in selfavoiding walks, lattice paths and walks with several step vectors. Many open problems are posted.
Title:  The enumeration of lattice paths and walks. 
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Name(s): 
Gao, Shanzhen. Charles E. Schmidt College of Science Department of Mathematical Sciences 

Type of Resource:  text  
Genre:  Electronic Thesis Or Dissertation  
Date Issued:  2011  
Publisher:  Florida Atlantic University  
Physical Form:  electronic  
Extent:  vii, 101 p. : ill.  
Language(s):  English  
Summary:  A wellknown long standing problem in combinatorics and statistical mechanics is to find the generating function for selfavoiding walks (SAW) on a twodimensional lattice, enumerated by perimeter. A SAW is a sequence of moves on a square lattice which does not visit the same point more than once. It has been considered by more than one hundred researchers in the pass one hundred years, including George Polya, Tony Guttmann, Laszlo Lovasz, Donald Knuth, Richard Stanley, Doron Zeilberger, Mireille BousquetMlou, Thomas Prellberg, Neal Madras, Gordon Slade, Agnes Dit tel, E.J. Janse van Rensburg, Harry Kesten, Stuart G. Whittington, Lincoln Chayes, Iwan Jensen, Arthur T. Benjamin, and many others. More than three hundred papers and a few volumes of books were published in this area. A SAW is interesting for simulations because its properties cannot be calculated analytically. Calculating the number of selfavoiding walks is a common computational problem. A recently proposed model called prudent selfavoiding walks (PSAW) was first introduced to the mathematics community in an unpublished manuscript of Pra, who called them exterior walks. A prudent walk is a connected path on square lattice such that, at each step, the extension of that step along its current trajectory will never intersect any previously occupied vertex. A lattice path composed of connected horizontal and vertical line segments, each passing between adjacent lattice points. We will discuss some enumerative problems in selfavoiding walks, lattice paths and walks with several step vectors. Many open problems are posted.  
Identifier:  751980598 (oclc), 3183129 (digitool), FADT3183129 (IID), fau:3709 (fedora)  
Note(s): 
by Shanzhen Gao. Thesis (Ph.D.)Florida Atlantic University, 2011. Includes bibliography. Electronic reproduction. Boca Raton, Fla., 2011. Mode of access: World Wide Web. 

Subject(s): 
Combinatorial analysis Approximation theory Mathematical statistics Limit theorems (Probabilty theory) 

Persistent Link to This Record:  http://purl.flvc.org/FAU/3183129  
Use and Reproduction:  http://rightsstatements.org/vocab/InC/1.0/  
Host Institution:  FAU 