COMBINATORICAL TECHNIQUES FOR ENUMERATION OF BISHOP/ROOK MOVEMENTS

This book is to provide the reader with basic concepts of polynomial generated by bishop/rook on a chess board with non-attacking bishop/rook within a forbidden space. The subject is so vast that in any introductory text, such as this, the discussion of various topics needs to be limited. Attempts have been made to present a variety of materials within a limited structure. References are indicated at the end to provide the reader with exhaustive treatment of the bishop/rook polynomial. However, this book explain wonderfully the bishop/rook and its movements to capture pieces in the same direction as the bishop/rook, and its counting techniques associated with the positions. It presents the basis of a chess board with research report in five parts; firstly, as enumerative techniques, secondly, application of generating functions; thirdly, as a rational function that generates a Laurent series that is algebraic; fourthly, as a board that decomposes into n-disjoint sub-boards; and fifthly, as a movement that generates a finite sum of terms. Finally, this chess polynomial can be comprehensively described by the key areas of a chess placement on a chess board with forbidden spaces.