Resumen de Extremal t-intersecting sub-families of hereditary families

Peter Borg

• 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