www-ai.cs.tu-dortmund.de/LEHRE/PG/PG445/literatur/goethals_2002a.pdf
3(13) =
( 5 4
) +
( 3 3
) = 6 and the
maximum number of candidate patterns of size 5 is KK 5 3(13) =
( 5 5
) = 1. This
is tight indeed, because
C4(L) = {{4, 3, 2, 1}, {5, 3, 2, 1}, {5, 4, 2, 1}, {5, 4, 3, [...] 2, 1}, {4, 3, 1}, {4, 3, 2}, {5, 2, 1}, {5, 3, 1}, {5, 3, 2}, {5, 4, 1}, {5, 4, 2}, {5, 4, 3}, {6, 2, 1}, {6, 3, 1}, {6, 3, 2}}.
The 3-canonical representation of 13 is ( 5 3
) +
( 3 2
) and hence the maximum [...] consist of all 19 3-subsets of {1, 2, 3, 4, 5} and {3, 4, 5, 6, 7} plus the sets {5, 7, 8} and {5, 8, 9}. Because 21 =
( 6 3
) +
( 2 2
) , we have KK 4
3(21) = 15, KK 5
3(21) = 6 and KK 6 3(21) = 1. On the other …