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مسألة ال-n ملكة
Other Title(s)
n-queen problem
Joint Authors
الراشد، شوقي محمد
أبو صافي، محمد
Source
مجلة جامعة دمشق للعلوم الأساسية
Issue
Vol. 37, Issue 1 (31 Jan. 2021), pp.165-189, 25 p.
Publisher
Publication Date
2021-01-31
Country of Publication
Syria
No. of Pages
25
Main Subjects
Abstract EN
The n-queen problem is one of the problems that can be solved using mathematical concepts, (where is a positive integer), where there are many methods to solve this problem as backtracking search technique[2, 9] and using global parallel genetic algorithm[3] and dynamic programming[10] and using DFS and BFS algorithms[12].
In this paper, we have studied some computation related to the chessboard, and we computed the number of squares associated and disassociated with square on a chessboard of size according to the queen's movement throught the theorms (1),(2) and (3) and apply it by the implementation on example for a chessboard of size , to represent this problem algebraically we used some concepts of computation in commutative algebra to solve the n-queen problem which are the concept of graded and the standard graded of rings, the hilbert series of graded rings, the dimension and multiplicity of the ring, additionally to the concept of the combinatorial dimension of an affine algebras.
we connected between queen's movement on the chessboard and the graph by the definition of the queen's graph and coloring it in special case.
using the computer algebra system SINGULAR[15], combinatorial dimension and we found the maximum number of queens can be placed on a chessboard so that no two of them attack one another in general case.
American Psychological Association (APA)
أبو صافي، محمد والراشد، شوقي محمد. 2021. مسألة ال-n ملكة. مجلة جامعة دمشق للعلوم الأساسية،مج. 37، ع. 1، ص ص. 165-189.
https://search.emarefa.net/detail/BIM-1275339
Modern Language Association (MLA)
أبو صافي، محمد والراشد، شوقي محمد. مسألة ال-n ملكة. مجلة جامعة دمشق للعلوم الأساسية مج. 37، ع. 1 (2021)، ص ص. 165-189.
https://search.emarefa.net/detail/BIM-1275339
American Medical Association (AMA)
أبو صافي، محمد والراشد، شوقي محمد. مسألة ال-n ملكة. مجلة جامعة دمشق للعلوم الأساسية. 2021. مج. 37، ع. 1، ص ص. 165-189.
https://search.emarefa.net/detail/BIM-1275339
Data Type
Journal Articles
Language
Arabic
Notes
يتضمن مراجع ببليوجرافية : ص. 189
Record ID
BIM-1275339