منابع مشابه
Queens on Non-square Tori
We prove that for m < n, the n × m rectangular toroidal chessboard admits gcd(m,n) nonattacking queens except in the case m = 3, n = 6. The classical n-queens problem is to place n queens on the n × n chessboard such that no pair is attacking each other. Solutions for this problem exist for all for n = 2, 3 [1]. The queens problem on a rectangular board is of little interest; on the n ×m board ...
متن کاملA q - QUEENS PROBLEM . II . THE SQUARE BOARD August
We apply to the n × n chessboard the counting theory from Part I for nonattacking placements of chess pieces with unbounded straight-line moves, such as the queen. Part I showed that the number of ways to place q identical nonattacking pieces is given by a quasipolynomial function of n of degree 2q, whose coefficients are (essentially) polynomials in q that depend cyclically on n. Here we study...
متن کاملYokohama, 236–0027
In this paper we revisit the isomorphism SU(2) ⊗ SU(2) ∼= SO(4) to apply to some subjects in Quantum Computation and Mathematical Physics. The unitary matrix Q by Makhlin giving the isomorphism as an adjoint action is studied and generalized from a different point of view. Some problems are also presented. In particular, the homogeneous manifold SU(2n)/SO(2n) which characterizes entanglements i...
متن کاملQueens ∗
A large scholarship claims that states led by women are less conflictual than states led by men. However, it is theoretically unclear why female leaders would favor more conciliatory war policies. And, it is empirically challenging to identify the effect of female rule, since women may gain power disproportionately during periods of peace. We surmount this challenge by exploiting features of he...
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: Journal of the Illuminating Engineering Institute of Japan
سال: 1999
ISSN: 0019-2341,1349-838X,2185-1506
DOI: 10.2150/jieij1980.83.9_716