Displaying similar documents to “Dot product rearrangements.”

The visibility parameter for words and permutations

Ligia Cristea, Helmut Prodinger (2013)

Open Mathematics

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We investigate the visibility parameter, i.e., the number of visible pairs, first for words over a finite alphabet, then for permutations of the finite set {1, 2, …, n}, and finally for words over an infinite alphabet whose letters occur with geometric probabilities. The results obtained for permutations correct the formula for the expectation obtained in a recent paper by Gutin et al. [Gutin G., Mansour T., Severini S., A characterization of horizontal visibility graphs and combinatorics...

Multigeometric sequences and Cantorvals

Artur Bartoszewicz, Małgorzata Filipczak, Emilia Szymonik (2014)

Open Mathematics

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For a sequence x ∈ l 10, one can consider the achievement set E(x) of all subsums of series Σn=1∞ x(n). It is known that E(x) has one of the following structures: a finite union of closed intervals, a set homeomorphic to the Cantor set, a set homeomorphic to the set T of subsums of Σn=1∞ x(n) where c(2n − 1) = 3/4n and c(2n) = 2/4n (Cantorval). Based on ideas of Jones and Velleman [Jones R., Achievement sets of sequences, Amer. Math. Monthly, 2011, 118(6), 508–521] and Guthrie and Nymann...

Classifications and characterizations of Baire-1 functions

Persephone Kiriakouli (1998)

Commentationes Mathematicae Universitatis Carolinae

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Kechris and Louveau in [5] classified the bounded Baire-1 functions, which are defined on a compact metric space K , to the subclasses ℬ 1 ξ ( K ) , ξ < ω 1 . In [8], for every ordinal ξ < ω 1 we define a new type of convergence for sequences of real-valued functions ( ξ -uniformly pointwise) which is between uniform and pointwise convergence. In this paper using this type of convergence we obtain a classification of pointwise convergent sequences of continuous real-valued functions defined on a compact metric...