| Title:
|
On relations between $f$-density and $(R)$-density (English) |
| Author:
|
Kijonka, Václav |
| Language:
|
English |
| Journal:
|
Acta Mathematica Universitatis Ostraviensis |
| ISSN:
|
1214-8148 |
| Volume:
|
15 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
15-20 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper it is discus a relation between $f$-density and $(R)$-density. A generalization of Šalát's result concerning this relation in the case of asymptotic density is proved. (English) |
| Keyword:
|
$f$-density |
| Keyword:
|
asymptotic density |
| Keyword:
|
weighted density |
| Keyword:
|
strong quotient base |
| Keyword:
|
$(R)$-density |
| MSC:
|
11B05 |
| idZBL:
|
Zbl 1235.11016 |
| idMR:
|
MR2418778 |
| . |
| Date available:
|
2009-12-29T09:22:09Z |
| Last updated:
|
2015-03-15 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137491 |
| . |
| Reference:
|
[1] Mišík L.: Sets of positive integers with prescribed values of densities.Math. Slovaca 52 (2002), 289-296 MR 1936334 |
| Reference:
|
[2] Mišík L., Tóth J. T.: Logarithmic density of sequence of integers and density of its ratio set.Journal de Theorie des Nombers de Bordeaux 15 (2003), 309-318. MR 2019018 |
| Reference:
|
[3] Strauch O., Tóth J. T.: Asymptotic density of A c N and density of the ratio set R(A).Acta Arith. 87 (1998), 67-78. MR 1659159 |
| Reference:
|
[4] Strauch O., Tóth J. T.: Corrigendum to Theorem 5 of the paper "Asymptotic density of ACN and density of the ratio set R(A)".Acta Arith. 87 (1998), 67-78, Acta Arith. 103.2 (2002), 191-200. MR 1904872 |
| Reference:
|
[5] Šalát T.: On ratio sets of sets of natural numbers.Acta Arith. 15 (1969), 273-278. MR 0242756 |
| Reference:
|
[6] Šalát T.: Quotientbasen und (R)-dichte Mengen.Acta Arith. 19 (1971), 63-78. Zbl 0218.10071, MR 0292788 |
| . |
