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- W2611808961 abstract "Abstract We show how to compute the permanent of an n × n integer matrix modulo p k in time n k + O ( 1 ) if p = 2 and in time 2 n / exp { Ω ( γ 2 n / p log p ) } if p is an odd prime with k p n , where γ = 1 − k p / n . Our algorithms are based on Ryser's formula, a randomized algorithm of Bax and Franklin, and exponential-space tabulation. Using the Chinese remainder theorem, we conclude that for each δ > 0 we can compute the permanent of an n × n integer matrix in time 2 n / exp { Ω ( δ 2 n / β 1 / ( 1 − δ ) log β ) } , provided there exists a real number β such that | per A | ≤ β n and β ≤ ( 1 44 δ n ) 1 − δ ." @default.
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- W2611808961 date "2017-09-01" @default.
- W2611808961 modified "2023-09-24" @default.
- W2611808961 title "Computing the permanent modulo a prime power" @default.
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- W2611808961 doi "https://doi.org/10.1016/j.ipl.2017.04.015" @default.
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