On difference sets of sets of positive integers

Martin Máčaj; Milan Paštéka; Tibor Šalát; Marek Žabka

Mathematica Slovaca (2003)

  • Volume: 53, Issue: 2, page 129-144
  • ISSN: 0232-0525

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Máčaj, Martin, et al. "On difference sets of sets of positive integers." Mathematica Slovaca 53.2 (2003): 129-144. <http://eudml.org/doc/34572>.

@article{Máčaj2003,
author = {Máčaj, Martin, Paštéka, Milan, Šalát, Tibor, Žabka, Marek},
journal = {Mathematica Slovaca},
keywords = {asymptotic density; uniform density; difference set},
language = {eng},
number = {2},
pages = {129-144},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {On difference sets of sets of positive integers},
url = {http://eudml.org/doc/34572},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Máčaj, Martin
AU - Paštéka, Milan
AU - Šalát, Tibor
AU - Žabka, Marek
TI - On difference sets of sets of positive integers
JO - Mathematica Slovaca
PY - 2003
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 53
IS - 2
SP - 129
EP - 144
LA - eng
KW - asymptotic density; uniform density; difference set
UR - http://eudml.org/doc/34572
ER -

References

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  2. BROWN T. C.-FREEDMAN A. R., The uniform density of sets of integers and Fermaťs last theorem, C R. Math. Rep. Acad. Sci. Canada 12 (1990), 1-6. (1990) MR1043085
  3. HARTER E., Differenzen von Mengen nicht negative Zahlen, J. Reine Angew. Math. 232 (1968), 112-116. (1968) MR0234902
  4. HOGGATT JR. V. E.-ALLADI K., Limiting ratios of convalued recursive sequences, Fibbonacci Quart. 15 (1977), 211-214. (1977) MR0480313
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  6. KUCZMA M. E.-KUCZMA M., An elementary proof and an extension of a theorem of Steinhaus, Glas. Mat. Ser. III 6(26) (1971), 11-18. (1971) Zbl0218.28001MR0304594
  7. KURATOWSKI C., Topologie I, PWN, Warszawa, 1958. (1958) 
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  10. OSTMANN H. H., Additive Zahlen - Theorie I, Springеr-Vеrlag, Bеrlin-Gottingen-Hеidelbеrg, 1956. (1956) MR0098721
  11. ŠALÁT T., On sets of distances of linear discontinuous, Časopis Pěst. Mat. 87 (1962), 4-16. (Russian) (1962) MR0180959
  12. ŠALÁT T., Über die Cantorsche Reihen, Czechoslovak Math. J. 18 (1968), 25-56. (1968) MR0223305
  13. SIERPIŃSKI W., Sur une propriete des nombres naturels, Elem. Math. 19 (1964), 27-29. (1964) Zbl0118.04908MR0160747
  14. SILVERMAN S., Intervals contained in arithmetic combinations of sets, Amer. Math. Monthly 102 (1995), 351-353. (1995) Zbl0838.28002MR1328021
  15. STEINHAUS H., Sur les distances des points des ensembles de measure positive, Fund. Math. 1 (1920), 99-104. (1920) 
  16. STOHR W., Geloste und ungeloste Fragen über Basen naturlichen Zahle - Reihe I; II, J. Reine Angew. Math. 194 (1955), 40-65; 111-140. (194) MR0075228
  17. VOLKMANN B., Zwei Bemerkungen über pseudorationale Mengen, J. Reine Angew. Math. 193 (1954), 126-128. (193) MR0064848
  18. VOROBJOV N. N., Fibonacci Numbers, Gos. Izd. Tech.-Teoret. Lit., Moscow-Lеningrad, 1951. (Russian) (1951) 
  19. WHEEDEN R. L.-ZYMUND A., Measure and Integrals, Marcel Dekker, New York, 1977. (1977) 
  20. VOLKMANN B., Über Hausdorfsche Dimensionen von Mengen, die durch Ziffereigenschaften charakterisiert sind, Math. Z. 59 (1953), 259-270. (1953) MR0059338

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