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Permutations preserving sums of rearranged real series

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Wituła R.

Open Mathematics

2013

tom 11

nr 5

956-965

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.

Some new facts about group 𝒢 generated by the family of convergent permutations

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Wituła R., Hetmaniok E., Słota D.

Open Mathematics

2017

tom 15

nr 1

568-577

The aim of this paper is to present some new and essential facts about group 𝒢 generated by the family of convergent permutations, i.e. the permutations on ℕ preserving the convergence of series of real terms. We prove that there exist permutations preserving the sum of series which do not belong to 𝒢. Additionally, we show that there exists a family G (possessing the cardinality equal to continuum) of groups of permutations on ℕ such that each one of these groups is different than 𝒢 and is composed only from the permutations preserving the sum of series. This result substantially strengthens some old Pleasants’ result.

Ograniczanie wyników

2 Open Mathematics

2 Wituła R.

1 Hetmaniok E.

1 Słota D.

1 2017

1 2013

Wyniki wyszukiwania

Permutations preserving sums of rearranged real series

Some new facts about group 𝒢 generated by the family of convergent permutations