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We prove that a random word of length n over a k-ary fixed alphabet contains, on expectation , Θ(√ n) distinct palindromic factors. We study this number of factors, E(n, k), in detail, showing that the limit lim n→∞ E(n, k)/ √ n does not exist for any k ≥ 2, lim inf n→∞ E(n, k)/ √ n = Θ(1), and lim sup n→∞ E(n, k)/ √ n = Θ(√ k). Such a complicated behaviour(More)
Palindromic length of a string is the minimum number of palindromes whose concatenation is equal to this string. The problem of finding the palindromic length drew some attention, and a few O(n logn) time online algorithms were recently designed for it. In this paper we present the first linear time online algorithm for this problem. 1998 ACM Subject(More)
The university has a very strong and internationally recognized algebraic school, which later extended to some areas of discrete math and theoretical computer science. Constructing and enumerating extremal power-free words. Defended Current Aleksandr Bocharov 2014-Probabilistic methods in combinatorics of words Mikhail Rubinchik 2013-Search and enumeration(More)