Hidden Structure in the Solutions Set of the N Queens Problem

2019/07/26 by T. E. Raptis, Raptis, T. E.
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Artificial Intelligence (cs.AI) #Cellular Automata and Applications #FOS: Computer and information sciences #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1909.05628

openalex publication_date 2019/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Some preliminary results are reported on the equivalence of any n-queens problem with the roots of a Boolean valued quadratic form via a generic dimensional reduction scheme. It is then proven that the solutions set is encoded in the entries of a special matrix. Further examination reveals a direct association with pointwise Boolean fractal operators applied on certain integer sequences associated with this matrix suggesting the presence of an underlying special geometry of the solutions set.

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