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On the Distribution of non-attacking Bishops on a Chessboard C

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Ansari Wahid, Shanaz

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Abstract

It is shown how the placement of non-attacking bishops on a chessboard C is related to the matching polynomial of a bipartite graph. Reduction algorithms for finding the bishop polynomial of C are given. We interpret combinatorially the coefficients of this polynomial and construct some interesting boards. Some applications of the bishop polynomials are given.
Se muestra cómo la colocación de alfiles que no atacan en un tablero de ajedrez C se relaciona con el polinomio de apareamiento de un grafo bipartito. Se dan algoritmos de reducción para encontrar el polinomio del alfil de C. Se interpretan combinatoriamente los coeficientes de este polinomio y se construyen algunos tableros interesantes. Se dan algunas aplicaciones de los polinomios de alfiles.

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http://revistas.ucr.ac.cr/index.php/matematica/article/view/197

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