منابع مشابه
Generating SIMD Vectorized Permutations
This paper introduces a method to generate efficient vectorized implementations of small stride permutations using only vector load and vector shuffle instructions. These permutations are crucial for highperformance numerical kernels including the fast Fourier transform. Our generator takes as input only the specification of the target platform’s SIMD vector ISA and the desired permutation. The...
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We show that the Möbius function of an interval in a permutation poset where the lower bound is sum (resp. skew) indecomposable depends solely on the sum (resp. skew) indecomposable permutations contained in the upper bound, and that this can simplify the calculation of the Möbius sum. For increasing oscillations, we give a recursion for the Möbius sum which only involves evaluating simple ineq...
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A permutation a1a2 . . . an is indecomposable if there does not exist p < n such that a1a2 . . . ap is a permutation of {1, 2, . . . , p}. We compute the asymptotic probability that a permutation of Sn with m cycles is indecomposable as n goes to infinity with m/n fixed. The error term is O( log(n−m) n−m ). The asymptotic probability is monotone in m/n, and there is no threshold phenomenon: it ...
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Given (n; k) with n k 2 and k 6 = 3, we show how to generate all permutations of n objects (each exactly once) so that successive permutations diier in exactly k positions, as do the rst and last permutations. This solution generalizes known results for the speciic cases where k = 2 and k = n. When k = 3, we show that it is possible to generate all even (odd) permutations of n objects so that s...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2006
ISSN: 0012-365X
DOI: 10.1016/j.disc.2006.01.005