The Family F of Permutations of ℕ
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Roman Wituła
Abstract
The paper is sacrificed to discussing the property of some special subfamily F of the family of all permutations of ℕ, especially in the context of the fundamental properties of families C and D of the, so called, convergent and divergent permutations, in other words, permutations preserving or not preserving the convergence of the rearranged real series, respectively. Family F is the subgroup of the group G generated by C. In the paper we will prove, among others, that F ⊂ C−1 ◦ C and F \ (C ◦ C−1) ≠ ∅. So, in particular we have G ≠ C◦C−1. The family F is neither the subset nor superset of any of the families C, D and C−1. By using the permutations belonging to the family F we receive the strengthening of some Kronrod’s theorems (which are the generalizations of the Riemann Derangement Theorem).
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Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Radius, Diameter and the Degree Sequence of a Graph
- On Primary Ideals in Posets
- Characterization of the Set of Regular Elements in Ordered Semigroups
- Tame Automorphisms with Multidegrees in the Form of Arithmetic Progressions
- A Result Concerning Additive Mappings in Semiprime Rings
- Characterizing Jordan Derivations of Matrix Rings Through Zero Products
- Existence Results for Impulsive Nonlinear Fractional Differential Equations With Nonlocal Boundary Conditions
- The Radon-Nikodym Property and the Limit Average Range
- A Hake-Type Theorem for Integrals with Respect to Abstract Derivation Bases in the Riesz Space Setting
- On Booth Lemniscate and Hadamard Product of Analytic Functions
- Recursion Formulas for Srivastava Hypergeometric Functions
- Regularly Varying Solutions of Half-Linear Diffferential Equations with Retarded and Advanced Arguments
- Singular Degenerate Differential Operators and Applications
- The Interior Euler-Lagrange Operator in Field Theory
- On Selections of Set-Valued Maps Satisfying Some Inclusions in a Single Variable
- The Family F of Permutations of ℕ
- Summation Process of Positive Linear Operators in Two-Dimensional Weighted Spaces
- On Iλ-Statistical Convergence in Locally Solid Riesz Spaces
- Some Norm one Functions of the Volterra Operator
- Some Results on Absolute Retractivity of the Fixed Points Set of KS-Multifunctions
- Convexity in the Khalimsky Plane
- Natural Boundary Conditions in Geometric Calculus of Variations
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