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On the permanent of Sylvester-Hadamard matrices

Abstract : We prove a conjecture due to Wanless about the permanent of Hadamard matrices in the particular case of Sylvester-Hadamard matrices. Namely we show that for all n greater or equal to 2, the dyadic valuation of the permanent of the Sylvester-Hadamard matrix of order n is equal to the dyadic valuation of n!. As a consequence, the permanent of the Sylvester-Hadamard matrix of order n doesn't vanish for n greater or equal to 2.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-02316978
Contributor : Ulysse Chabaud <>
Submitted on : Tuesday, October 15, 2019 - 5:05:12 PM
Last modification on : Thursday, October 17, 2019 - 1:26:29 AM

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  • HAL Id : hal-02316978, version 1
  • ARXIV : 1802.08001

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Ulysse Chabaud. On the permanent of Sylvester-Hadamard matrices. 2019. ⟨hal-02316978⟩

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