On commutation properties of the composition relation of convergent and divergent permutations (PART I)

In: Tatra Mountains Mathematical Publications, vol. 58, no. 1

Edyta Hetmaniok - Damian Słota - Roman Wituła

Detaily:

Rok, strany: 2014, 13 - 22

Kľúčové slová:

commutation of composition of permutations, convergent permutations, divergent permutations.

O článku:

In the paper we present the selected properties of composition relation of the convergent and divergent permutations connected with commutation. We note that a permutation on $\mathbb{N}$ is called the convergent permutation if for each convergent series $∑ a_n$ of real terms, the $p$-rearranged series $∑ a_p(n)$ is also convergent. All the other permutations on $\mathbb{N}$ are called the divergent permutations. We have proven, among others, that, for many permutations $p$ on $\mathbb{N}$, the family of divergent permutations $q$ on $\mathbb{N}$ commuting with $p$ possesses cardinality of the continuum. For example, the permutations $p$ on $\mathbb{N}$ having finite order possess this property. On the other hand, an example of a convergent permutation which commutes only with some convergent permutations is also presented.

Ako citovať:

ISO 690:

Hetmaniok, E., Słota, D., Wituła, R. 2014. On commutation properties of the composition relation of convergent and divergent permutations (PART I). In Tatra Mountains Mathematical Publications, vol. 58, no.1, pp. 13-22. 1210-3195.

APA:

Hetmaniok, E., Słota, D., Wituła, R. (2014). On commutation properties of the composition relation of convergent and divergent permutations (PART I). Tatra Mountains Mathematical Publications, 58(1), 13-22. 1210-3195.