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2013 | 11 | 5 | 956-965
Tytuł artykułu

Permutations preserving sums of rearranged real series

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Treść / Zawartość
Warianty tytułu
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.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
5
Strony
956-965
Opis fizyczny
Daty
wydano
2013-05-01
online
2013-03-14
Twórcy
Bibliografia
  • [1] Agnew R.P., Permutations preserving convergence of series, Proc. Amer. Math. Soc., 1955, 6(4), 563–564 http://dx.doi.org/10.1090/S0002-9939-1955-0071559-4
  • [2] Garibay F., Greenberg P., Reséndis L., Rivaud J.J., The geometry of sum-preserving permutations, Pacific J. Math., 1988, 135(2), 313–322 http://dx.doi.org/10.2140/pjm.1988.135.313
  • [3] Guha U.C., On Levi’s theorem on rearrangement of convergent series, Indian J. Math., 1967, 9, 91–93
  • [4] Hu M.C., Wang J.K., On rearrangements of series, Bull. Inst. Math. Acad. Sinica, 1979, 7(4), 363–376
  • [5] Kronrod A., On permutation of terms of numerical series, Mat. Sbornik, 1946, 18(60), 237–280 (in Russian)
  • [6] Levi F.W., Rearrangement of convergent series, Duke Math. J., 1946, 13, 579–585 http://dx.doi.org/10.1215/S0012-7094-46-01348-8
  • [7] Pleasants P.A.B., Rearrangements that preserve convergence, J. London Math. Soc., 1977, 15(1), 134–142 http://dx.doi.org/10.1112/jlms/s2-15.1.134
  • [8] Pleasants P.A.B., Addendum: “Rearrangements that preserve convergence”, J. Lond. Math. Soc., 1978, 18(3), 576 http://dx.doi.org/10.1112/jlms/s2-18.3.576-s
  • [9] Schaefer P., Sum-preserving rearrangements of infinite series, Amer. Math. Monthly, 1981, 88(1), 33–40 http://dx.doi.org/10.2307/2320709
  • [10] Stoller G.S., The convergence-preserving rearrangements of real infinite series, Pacific J. Math., 1977, 73(1), 227–231 http://dx.doi.org/10.2140/pjm.1977.73.227
  • [11] Wituła R., Convergence-preserving functions, Nieuw Arch. Wisk., 1995, 13(1), 31–35
  • [12] Wituła R., The Riemann theorem and divergent permutations, Colloq. Math., 1995, 69(2), 275–287
  • [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
  • [18] Nash-Williams C.St.J.A., White D.J., An application of network flows to rearrangement of series, J. Lond. Math. Soc., 1999, 59(2), 637–646 http://dx.doi.org/10.1112/S0024610799007292
  • [19] Nash-Williams C.St.J.A., White D.J., Rearrangement of vector series. I, Math. Proc. Cambridge Philos. Soc., 2001, 130(1), 89–109 http://dx.doi.org/10.1017/S0305004100004813
  • [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
Typ dokumentu
Bibliografia
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bwmeta1.element.doi-10_2478_s11533-012-0156-x
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