منابع مشابه
Common intervals in permutations
An interval of a permutation is a consecutive substring consisting of consectuve symbols. For example, 4536 is an interval in the permutation 71453682. These arise in genetic applications. For the applications, it makes sense to generalize so as to allow gaps of bounded size δ− 1, both in the locations and the symbols. For example, 4527 has gaps bounded by 1 (since 3 and 6 are missing) and is t...
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For π ∈ Sn, let d(π) be the arithmetic average of {|i − π(i)|; 1 ≤ i ≤ n}. Then 0 ≤ d(π)/n ≤ 1/2, the expected value of d(π)/n approaches 1/3 as n approaches infinity, and most permutations have d(π)/n close to 1/3. We also describe all permutations with d(π)/n = 1/2. Let s(π) and s∗(π) be the arithmetic and geometric averages of {|π(i) − π(i + 1)|; 1 ≤ i < n}, respectively. Let M, M∗ be the ma...
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Common intervals of K permutations over the same set of n elements were firstly investigated by T. Uno and M.Yagiura (Algorithmica, 26:290:309, 2000), who proposed an efficient algorithm to find common intervals when K = 2. Several particular classes of intervals have been defined since then, e.g. conserved intervals and nested common intervals, with applications mainly in genome comparison. Ea...
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1. Fundamental theorem. In a recent paper f I have proved the theorem that if a lacunary trigonometric series CO (1) X(a* cos nk6 + bk sin nk9) (nk+x/nk > q > 1, 0 ^ 0 ^ 2ir) 4-1 has its partial sums uniformly bounded on a set of 0 of positive measure, then the series (2) ¿(a*2 + bk2) k-l converges. The proof was based on the following lemma (which was not stated explicitly but is contained in ...
متن کاملOn lacunary Toeplitz determinants
By using Riemann–Hilbert problem based techniques, we obtain the asymptotic expansion of lacunary Toeplitz determinants detN [ cla−mb [ f ] ] generated by holomorhpic symbols, where la = a (resp. mb = b) except for a finite subset of indices a = h1, . . . , hn (resp. b = t1, . . . , tr). In addition to the usual Szegö asymptotics, our answer involves a determinant of size n + r.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1995
ISSN: 0002-9947
DOI: 10.2307/2155216