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    Item type:Publication, Access status: with files ,
    r-Cross t-intersecting families via necessary intersection points
    (Wiley, 2023-02-20)
    Gupta, Pranshu
    ;
    Mogge, Yannick
    ;
    Piga, Simón
    ;
    Schülke, Bjarne
    Given integers (Formula presented.) and (Formula presented.) we call families (Formula presented.) (Formula presented.) -cross (Formula presented.) -intersecting if for all (Formula presented.), (Formula presented.), we have (Formula presented.). We obtain a strong generalisation of the classic Hilton–Milner theorem on cross-intersecting families. In particular, we determine the maximum of (Formula presented.) for (Formula presented.) -cross (Formula presented.) -intersecting families in the cases when these are (Formula presented.) -uniform families or arbitrary subfamilies of (Formula presented.). Only some special cases of these results had been proved before. We obtain the aforementioned theorems as instances of a more general result that considers measures of (Formula presented.) -cross (Formula presented.) -intersecting families. This also provides the maximum of (Formula presented.) for families of possibly mixed uniformities (Formula presented.).
    Publicationtype: Journal Article
      47  1919
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    Item type:Publication, Access status: without files ,
    Maximum size of r-cross t-intersecting families
    (2021-05)
    Gupta, Pranshu
    ;
    Mogge, Yannick
    ;
    Piga, Simón
    ;
    Schülke, Bjarne
    Given r families of subsets of a fixed n-set, we say that they are r-cross t-intersecting if for every choice of representatives, exactly one from each family, the common intersection of these representatives is of size at least t. We obtain a generalisation of a result by Hilton and Milner on cross intersecting families. In particular, we determine the maximum possible sum of the sizes of non-empty r-cross t-intersecting families in the case when all families are k-uniform and in the case when they are arbitrary subfamilies of the power set. Only some special cases of these results had been proved before. The method we use also yields more general results concerning measures of families instead of their sizes.
    Publicationtype: Conference Paper
      155