منابع مشابه
A 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...
متن کاملA q-QUEENS PROBLEM IV. QUEENS, BISHOPS, NIGHTRIDERS (AND ROOKS)
Parts I–III showed that the number of ways to place q nonattacking queens or similar chess pieces on an n × n chessboard is a quasipolynomial function of n whose coefficients are essentially polynomials in q and, for pieces with some of the queen’s moves, proved formulas for these counting quasipolynomials for small numbers of pieces and highorder coefficients of the general counting quasipolyn...
متن کاملOn the diagonal queens domination problem
It is shown that the problem of covering an n x n chessboard with a minimum number of queens on a major diagonal is related to the number-theoretic function rj(n), the smallest number of integers in a subset of {l,..., n} which must contain three terms in arithmetic progression. Several problems concerning the covering of chessboards by queens have been studied in the literature [2]. In this no...
متن کاملA 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, ...
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ژورنال
عنوان ژورنال: INFORMS Transactions on Education
سال: 2002
ISSN: 1532-0545,1532-0545
DOI: 10.1287/ited.2.3.101