Permutations preserving sums of rearranged real series

Roman Wituła

Open Mathematics (2013)

  • Volume: 11, Issue: 5, page 956-965
  • ISSN: 2391-5455

Abstract

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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 𝔖 0 , introduced by it, are investigated.

How to cite

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Roman Wituła. "Permutations preserving sums of rearranged real series." Open Mathematics 11.5 (2013): 956-965. <http://eudml.org/doc/268997>.

@article{RomanWituła2013,
abstract = {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.},
author = {Roman Wituła},
journal = {Open Mathematics},
keywords = {Permutations preserving sums of series; Convergent permutations; Divergent permutations; permutations preserving sums of series; convergent permutations; divergent permutations; rearranged series},
language = {eng},
number = {5},
pages = {956-965},
title = {Permutations preserving sums of rearranged real series},
url = {http://eudml.org/doc/268997},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Roman Wituła
TI - Permutations preserving sums of rearranged real series
JO - Open Mathematics
PY - 2013
VL - 11
IS - 5
SP - 956
EP - 965
AB - 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.
LA - eng
KW - Permutations preserving sums of series; Convergent permutations; Divergent permutations; permutations preserving sums of series; convergent permutations; divergent permutations; rearranged series
UR - http://eudml.org/doc/268997
ER -

References

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  9. [9] Schaefer P., Sum-preserving rearrangements of infinite series, Amer. Math. Monthly, 1981, 88(1), 33–40 http://dx.doi.org/10.2307/2320709 Zbl0455.40007
  10. [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 Zbl0364.40001
  11. [11] Wituła R., Convergence-preserving functions, Nieuw Arch. Wisk., 1995, 13(1), 31–35 Zbl0858.40004
  12. [12] Wituła R., The Riemann theorem and divergent permutations, Colloq. Math., 1995, 69(2), 275–287 Zbl0840.40002
  13. [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 Zbl1187.40007
  14. [14] Wituła R., On algebraic properties of some subsets of families of convergent and divergent permutations (manuscript) Zbl1313.40004
  15. [15] Wituła R., The algebraic properties of the convergent and divergent permutations (manuscript) Zbl1313.40004
  16. [16] Wituła R., The family 𝔉 of permutations of ℕ (manuscript) 
  17. [17] Wituła R., Słota D., Seweryn R., On Erdös’ theorem for monotonic subsequences, Demonstratio Math., 2007, 40(2), 239–259 Zbl1129.05003
  18. [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 
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  20. [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 Zbl0984.40005

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