Atoms of families of sets

Abstract

An atom of a familyF= (A v :vI) of sets is a set of the form\(\bigcap\limits_\nu {(\nu \varepsilon N)A_\nu - \bigcup\limits_\nu {(\nu \varepsilon I - N)A_\nu } ,} \) where 0⊂NI. The note deals with upper and lower estimates of the possible number of non-empty atoms ofF in case theA v are parallelopipeds ind-dimensional space. Some estimates are best possible.

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Dedicated to Tibor Gallai on his seventieth birthday

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Rado, R. Atoms of families of sets. Combinatorica 2, 311–314 (1982). https://doi.org/10.1007/BF02579238

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AMS subject classification 1980

  • 04 A 20
  • 05 C 65
  • 51 M 05
  • 52 A 20