Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012, Number 2, Pages 20–24
This article is cited in 1 scientific paper (total in 1 paper)
Two-sided estimates for essential height in Shirshov's Height Theorem
M. I. Kharitonov
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
The paper is focused on two-sided estimates of the essential height in Shirshov's Height theorem. The notions of the selective height and strong $n$-divisibility directly related to the height and $n$-divisibility are introduced in the paper. We find lower and upper bounds for the selective height of non-strongly $n$-divided words over the words of length 2. These bounds differ by not more than twice for any $n$ and sufficiently large $l$. The case of words of length 3 is also studied. The case of words of length 2 can be generalized to the proof of a subexponential estimate in Shirshov's Height theorem. The proof uses the idea of Latyshev related to the use of Dilworth's theorem to the of non-$n$-divided words.
essential height, Shirshov's height theorem, combinatorics of words, $n$-divisibility, Dilworth's theorem.
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Moscow University Mathematics Bulletin, 2012, 67:2, 64–68
M. I. Kharitonov, “Two-sided estimates for essential height in Shirshov's Height Theorem”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012, no. 2, 20–24; Moscow University Mathematics Bulletin, 67:2 (2012), 64–68
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\paper Two-sided estimates for essential height in Shirshov's Height Theorem
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\jour Moscow University Mathematics Bulletin
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This publication is cited in the following articles:
M. I. Kharitonov, “Otsenki, svyazannye s teoremoi Shirshova o vysote”, Chebyshevskii sb., 15:4 (2014), 55–123
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