A new generalization of the Erdo¨s-Ko-Rado theorem
Journal of Combinatorial Theory Series A
An Erdo¨s-Ko-Rado theorem for integer sequences of given rank
European Journal of Combinatorics
The exact bound in the Erdo¨s—Ko—Rado theorem for cross-intersecting fami
Journal of Combinatorial Theory Series A
Regular Article: The Diametric Theorem in Hamming Spaces驴Optimal Anticodes
Advances in Applied Mathematics
Cross-intersecting families and primitivity of symmetric systems
Journal of Combinatorial Theory Series A
Cross-Intersecting Families of Partial Permutations
SIAM Journal on Discrete Mathematics
Cross-intersecting sub-families of hereditary families
Journal of Combinatorial Theory Series A
Independent sets in direct products of vertex-transitive graphs
Journal of Combinatorial Theory Series B
Nontrivial independent sets of bipartite graphs and cross-intersecting families
Journal of Combinatorial Theory Series A
The maximum sum and the maximum product of sizes of cross-intersecting families
European Journal of Combinatorics
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A k-signed r-set on[n]={1,...,n} is an ordered pair (A,f), where A is an r-subset of [n] and f is a function from A to [k]. Families A"1,...,A"p are said to be cross-intersecting if any set in any family A"i intersects any set in any other family A"j. 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.