Discrepancy of high-dimensional permutations
نویسندگان
چکیده
منابع مشابه
Monotone Subsequences in High-Dimensional Permutations
This paper is part of the ongoing effort to study high-dimensional permutations. We prove the analogue to the Erdős–Szekeres Theorem: For every k ≥ 1, every order-n k-dimensional permutation contains a monotone subsequence of length Ωk (√ n ) , and this is tight. On the other hand, and unlike the classical case, the longest monotone subsequence in a random kdimensional permutation of order n is...
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What is the higher-dimensional analog of a permutation? If we think of a permutation as given by a permutation matrix, then the following definition suggests itself: A d-dimensional permutation of order n is an n × n × . . . n = [n]d+1 array of zeros and ones in which every line contains a unique 1 entry. A line here is a set of entries of the form {(x1, . . . , xi−1, y, xi+1, . . . , xd+1)|n ≥...
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ژورنال
عنوان ژورنال: Discrete Analysis
سال: 2016
ISSN: 2397-3129
DOI: 10.19086/da.845