A history and a survey of lattice path enumeration

In celebration of the Sixth International Conference on Lattice Path Counting and Applications, it is befitting to review the history of lattice path enumeration and to survey how the topic has progressed thus far. We start the history with early games of chance specifically the ruin problem which l...

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Vydáno v:Journal of statistical planning and inference Ročník 140; číslo 8; s. 2237 - 2254
Hlavní autor: Humphreys, Katherine
Médium: Journal Article Konferenční příspěvek
Jazyk:angličtina
Vydáno: Kidlington Elsevier B.V 01.08.2010
Elsevier
Témata:
Combinatorics. Ordered structures
Exact sciences and technology
General topics
Lattice path
Mathematics
Method of images
Order, lattices, ordered algebraic structures
Probability and statistics
Reflection principle
Sciences and techniques of general use
Statistics
Lattice path
Method of images
Reflection principle
Brownian motion
Statistical method
Statistical decision
Sample survey
Physics
Lattice
ISSN:0378-3758, 1873-1171
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Shrnutí:In celebration of the Sixth International Conference on Lattice Path Counting and Applications, it is befitting to review the history of lattice path enumeration and to survey how the topic has progressed thus far. We start the history with early games of chance specifically the ruin problem which later appears as the ballot problem. We discuss André's Reflection Principle and its misnomer, its relation with the method of images and possible origins from physics and Brownian motion, and the earliest evidence of lattice path techniques and solutions. In the survey, we give representative articles on lattice path enumeration found in the literature in the last 35 years by the lattice, step set, boundary, characteristics counted, and solution method. Some of this work appears in the author's 2005 dissertation.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2010.01.020