Permutations preserving sums of rearranged real series

• Autorzy: Roman Wituła
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to discuss one of the most interesting and unsolved problems of the real series theory: rearrangements that preserve sums of series. Certain hypothesis about combinatorial description of the corresponding permutations is presented and basic algebraic properties of the family $\mathfrak{S}_0 $, introduced by it, are investigated.

Słowa kluczowe

EN

Permutations preserving sums of series; Convergent permutations; Divergent permutations

Kategorie tematyczne

• 05A99: None of the above, but in this section
• 40A05: Convergence and divergence of series and sequences

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 5
• Strony: 956-965

Daty

wydano

2013-05-01

online

2013-03-14

Twórcy

autor

Roman Wituła

• Silesian University of Technology

Bibliografia

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• [13] Wituła R., On the set of limit points of the partial sums of series rearranged by a given divergent permutation, J. Math. Anal. Appl., 2010, 362(2), 542–552 http://dx.doi.org/10.1016/j.jmaa.2009.09.028
• [14] Wituła R., On algebraic properties of some subsets of families of convergent and divergent permutations (manuscript)
• [15] Wituła R., The algebraic properties of the convergent and divergent permutations (manuscript)
• [16] Wituła R., The family \(\mathfrak{F}\) of permutations of ℕ (manuscript)
• [17] Wituła R., Słota D., Seweryn R., On Erdös’ theorem for monotonic subsequences, Demonstratio Math., 2007, 40(2), 239–259
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• [20] Nash-Williams C.St.J.A., White D.J., Rearrangement of vector series. II, Math. Proc. Cambridge Philos. Soc., 2001, 130(1), 111–134 http://dx.doi.org/10.1017/S0305004100004825

Identyfikatory

DOI

10.2478/s11533-012-0156-x