A BISHOP MOVEMENT ON A CHESS BOARD AS A RATIONAL FUNCTION GENERATE A LAURENT SERIES THAT IS ALGEBRAIC
Keywords:
Chess movements; Laurent series; Permutation; Power Series; Handamard product.Abstract
The purpose of this study was carried to examine the counting problems of non-attacking bishop placements on any chess board. The chess board for bishop placement with forbidden positions was considered as a diagonal movement to the right or to the left. We discussed the general movement of a bishop as a rational function of a power series on a chess board in variables s and t. Furthermore, we constructed the movement techniques of a bishop placements as rational function that generates a Laurent series that is algebraic. Finally, we applied it to combinatorial problems that generates’ the diagonal movement of a bishop to give the Laurent series that is algebraic over k (t).
