Hidden Structure in the Solutions Set of the N Queens Problem
This work provides incremental insights into the combinatorial structure of the N Queens problem, which is of interest to mathematicians and computer scientists studying puzzles and algorithms.
The paper tackled the N Queens problem by showing its equivalence to the roots of a Boolean quadratic form and encoding the solutions set in a special matrix, revealing an underlying geometry through associations with Boolean fractal operators.
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.