
EXAMPLE

In S_6, permutations with maximum strategic pile have either 5,6, or 10 available CDS contexts. Hence a_3 = #{5,6,10}.
For example, the permutation [6, 1, 4, 2, 5, 3] is in S_6 with maximum strategic pile, and it has 5 contexts: { (1,2),(3,4) ; (1,2),(4,5) ; (2,3),(4,5) ; (2,3),(5,6) ; (3,4),(5,6) } The permutation [6, 1, 5, 2, 4, 3] is in S_6 with maximum strategic pile, and it has 6 contexts: { (1,2),(4,5) ; (1,2),(5,6) ; (4,5),(5,6) ; (2,3),(3,4) ; (2,3),(4,5) ; (3,4),(4,5) } The permutation [6, 1, 3, 5, 2, 4] is in S_6 with maximum strategic pile, and it has 10 contexts (all possible pairs of the 5 pointers): { (1,2),(2,3) ; (1,2),(3,4) ; (1,2),(4,5) ; (1,2),(5,6) ; (2,3),(3,4) ; (2,3),(4,5) ; (2,3),(5,6) ; (3,4),(4,5) ; (3,4),(5,6) ; (4,5),(5,6) }
