Extremal t-intersecting sub-families of hereditary families

• Autores: Peter Borg
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 79, Nº 1, 2009, págs. 167-185
• Idioma: inglés
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• Resumen

  • A family of sets is said to be t-intersecting if any two sets in contain at least t common elements. A t-intersecting family is said to be trivial if there are at least t elements common to all its sets. A family is said to be hereditary if all subsets of any set in are in .

    For a finite family , let (s) be the family of s-element sets in , and let µ() be the size of a smallest set in that is not a subset of any other set in . For any two integers r and t with 1t

    We apply our main result to obtain new results on t-intersecting families of signed sets, permutations and separated sets. This work supports some open conjectures