The combinatorics of chessboards.
Item
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Title
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The combinatorics of chessboards.
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Identifier
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AAI9908387
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identifier
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9908387
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Creator
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Zhao, Kaiyan.
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Contributor
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Adviser: Michael Anshel
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Date
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1998
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Language
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English
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Publisher
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City University of New York.
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Subject
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Mathematics | Computer Science
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Abstract
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The classic combinatorial problem know as The n-Queens Problem is to find the number of arrangements of n queens on an n x n chessboard such that no queen attacks another. In addition to numerous papers on the topic, the problem has many extensions. Examples include The Toroidal n-Queens Problem: To find the number of arrangements of n queens on a toroidal n x n chessboard such that no queen attacks another, The Cylinder n-Queens Problem: To find a similar solution for a cylindrical n x n chessboard; The Minimum Queens Problem: To place fewer than n queens on an n x n chessboard so that none attacks another, but so that they also together attack every unoccupied cell; The Reflecting Queens Problem; The Queens on an Infinite Chessboard Problem; and many others. The classic problem and each of its variations contains unsolved problems.;In this paper, I present a new method for generating solutions to the classic problem using quasi-groups and I offer yet another extension to the problem, The Queens Problem on a Partial Chessboard, which is to arrange more than n queens on an n x n chessboard with m cells blocked such that no queen attacks another. Under what conditions do such arrangements exist? How many blocked cells are needed to yield solutions? I also present a computer simulation of the n-Queens Problem and of the Queens Problem on a Partial Chessboard that is a useful tool for mathematicians who study these problems.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
