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- W2000600113 abstract "For positive integers r and n with r⩽n, let Pr,n be the family of all sets {(1,y1),(2,y2),…,(r,yr)} such that y1,y2,…,yr are distinct elements of [n]={1,2,…,n}. Pn,n describes permutations of [n]. For r<n, Pr,n describes permutations of r-element subsets of [n]. Families A1,A2,…,Ak of sets are said to be cross-intersecting if, for any distinct i and j in [k], any set in Ai intersects any set in Aj. For any r, n and k⩾2, we determine the cases in which the sum of sizes of cross-intersecting sub-families A1,A2,…,Ak of Pr,n is a maximum, hence solving a recent conjecture (suggested by the author)." @default.
- W2000600113 created "2016-06-24" @default.
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- W2000600113 date "2010-05-01" @default.
- W2000600113 modified "2023-10-01" @default.
- W2000600113 title "Cross-intersecting families of permutations" @default.
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- W2000600113 doi "https://doi.org/10.1016/j.jcta.2009.07.003" @default.
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