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The family \textfrak{F} of permutations of $\mathbb{N}$

In: Mathematica Slovaca, vol. 65, no. 6
Roman Wituła
Detaily:
Rok, strany: 2015, 1457 - 1474
Kľúčové slová:
convergent permutations, divergent permutations, family \textfrak{F} of permutations of $\mathbb{N}$
O článku:
The paper is sacrificed to discussing the property of some special subfamily $\mathfrak{F}$ of the family of all permutations of $\mathbb{N}$, especially in the context of the fundamental properties of families $\mathfrak{C}$ and $\mathfrak{D}$ 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 $\mathfrak{F}$ is the subgroup of the group $\mathfrak{G}$ generated by $\mathfrak{C}$. In the paper we will prove, among others, that $\mathfrak{F}\subset\mathfrak{C}-1\circ\mathfrak{C}$ and $\mathfrak{F}\setminus(\mathfrak{C}\circ\mathfrak{C}-1) \neq \varnothing$. So, in particular we have $\mathfrak{G}\neq \mathfrak{C} \circ \mathfrak{C}-1$. The family $\mathfrak{F}$ is neither the subset nor superset of any of the families $\mathfrak{C}$, $\mathfrak{D}$ and $\mathfrak{C}-1$. By using the permutations belonging to the family $\mathfrak{F}$ we receive the strengthening of some Kronrod's theorems (which are the generalizations of the Riemann Derangement Theorem).
Ako citovať:
ISO 690:
Wituła, R. 2015. The family \textfrak{F} of permutations of $\mathbb{N}$. In Mathematica Slovaca, vol. 65, no.6, pp. 1457-1474. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0099

APA:
Wituła, R. (2015). The family \textfrak{F} of permutations of $\mathbb{N}$. Mathematica Slovaca, 65(6), 1457-1474. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0099
O vydaní:
Publikované: 1. 12. 2015