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JCT
2010

Multiple cross-intersecting families of signed sets

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Multiple cross-intersecting families of signed sets
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.
Peter Borg, Imre Leader
Added 28 Jan 2011
Updated 28 Jan 2011
Type Journal
Year 2010
Where JCT
Authors Peter Borg, Imre Leader
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