A $q$-Queens Problem. I. General Theory
نویسندگان
چکیده
منابع مشابه
A q-Queens Problem. I. General Theory
By means of the Ehrhart theory of inside-out polytopes we establish a general counting theory for nonattacking placements of chess pieces with unbounded straight-line moves, such as the queen, on a polygonal convex board. The number of ways to place q identical nonattacking pieces on a board of variable size n but fixed shape is (up to a normalization) given by a quasipolynomial function of n, ...
متن کاملA q - QUEENS PROBLEM I . GENERAL THEORY MARCH 3 , 2013
We establish a general counting theory for nonattacking placements of chess pieces with unbounded straight-line moves, such as the queen, and we apply the theory to square boards. We show that the number of ways to place q nonattacking queens on a chessboard of variable size n but fixed shape is a quasipolynomial function of n. The period of the quasipolynomial is bounded by a function of the q...
متن کاملA q - QUEENS PROBLEM I . GENERAL THEORY August
By means of the Ehrhart theory of inside-out polytopes we establish a general counting theory for nonattacking placements of chess pieces with unbounded straight-line moves, such as the queen, on a polygonal convex board. The number of ways to place q identical nonattacking pieces on a board of variable size n but fixed shape is (up to a normalization) given by a quasipolynomial function of n, ...
متن کاملA q-QUEENS PROBLEM III. PARTIAL QUEENS
Parts I and II showed that the number of ways to place q nonattacking queens or similar chess pieces on an n× n square chessboard is a quasipolynomial function of n in which the coefficients are essentially polynomials in q. We explore this function for partial queens, which are pieces like the rook and bishop whose moves are a subset of those of the queen. We compute the five highest-order coe...
متن کاملA q-QUEENS PROBLEM III. PARTIAL QUEENS
Parts I and II showed that the number of ways to place q nonattacking queens or similar chess pieces on an n× n square chessboard is a quasipolynomial function of n in which the coefficients are essentially polynomials in q. We explore this function for partial queens, which are pieces like the rook and bishop whose moves are a subset of those of the queen. We compute the five highest-order coe...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2014
ISSN: 1077-8926
DOI: 10.37236/4093