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ON THE EXISTENCE OF BINARY DE BRUIJN CYCLES UNDER THE FLIPPING EQUIVALENCE RELATION

机译:关于在翻转等价关系下的二元de bruijn循环的存在

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摘要

In this paper, we deal with the existence of binary De Bruijn cycle of order k under flipping equivalence relation, written as (k, ≈)-De Bruijn cycle, advocated by Hartke [1]. We construct some infinite families of (k, ≈)-De Bruijn cycles of small lengths n for odd k with k ≤ n ≤ k + 5, and for even k with k ≤ n ≤ k + 4, respectively. For k < 4, we prove the non-existence of (k, ≈)-De Bruijn cycle, and find the minimum lengths of (k, ≈)-De Bruijn cycles for k = 4 and 5 are all 6.
机译:在本文中,我们处理了在翻转等价关系下的二元de bruijn循环的存在,以(k,≈)-de bruijn循环编写,由Hartke [1]提倡。 我们构建了(k,≈)-de bruijn循环的一些无限族,分别为k≤n≤k + 5的奇数k,甚至分别具有k≤n≤k + 4的k。 对于k <4,我们证明(k,≈)-de bruijn循环的不存在,并找到k = 4和5的最小长度(k,≈)-de bruijn循环全部6。

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