Multiple cross-intersecting families of signed sets
نویسندگان
چکیده
A k-signed r-set on [n] = {1, ..., n} is an ordered pair (A, f), where A is an rsubset of [n] and f is a function from A to [k]. Families A1, ...,Ap are said to be cross-intersecting if any set in any family Ai intersects any set in any other family Aj . Hilton proved a sharp bound for the sum of sizes of cross-intersecting families of r-subsets of [n]. Our aim is to generalise Hilton's bound to one for families of k-signed r-sets on [n]. The main tool developed is an extension of Katona's cyclic permutation argument.
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 117 شماره
صفحات -
تاریخ انتشار 2010