从次皮质重建高皮质

IF 0.9 2区 数学 Q2 MATHEMATICS Journal of Combinatorial Theory Series A Pub Date : 2024-10-22 DOI:10.1016/j.jcta.2024.105966
Wenjie Zhong , Xiande Zhang
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引用次数: 0

摘要

对于给定的 n,使得长度为 n 的每个序列都由其所有 k 个子序列的多集决定的最小数 k 是多少?这被称为序列重构的 k 层问题,并已被推广到二维情况--从子矩阵重构 n×n 矩阵。之前的研究表明,对于序列,最小的 k 至多为 O(n12),而对于矩阵,则至多为 O(n23)。我们研究了一般维数为 d 的 k 层问题,并证明了从其所有阶数为 k 的子超矩阵的多集重构任何阶数为 n 的 d 维超矩阵时,最小 k 至多为 O(ndd+1)。
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Reconstruction of hypermatrices from subhypermatrices
For a given n, what is the smallest number k such that every sequence of length n is determined by the multiset of all its k-subsequences? This is called the k-deck problem for sequence reconstruction, and has been generalized to the two-dimensional case – reconstruction of n×n-matrices from submatrices. Previous works show that the smallest k is at most O(n12) for sequences and at most O(n23) for matrices. We study this k-deck problem for general dimension d and prove that, the smallest k is at most O(ndd+1) for reconstructing any d dimensional hypermatrix of order n from the multiset of all its subhypermatrices of order k.
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来源期刊
CiteScore
2.90
自引率
9.10%
发文量
94
审稿时长
12 months
期刊介绍: The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.
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