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COMMENT
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.............................C(0,0)*C(10,5)
......................C(1,0)*C(9,5)...C(1,1)*C(9,4)
...............C(2,0)*C(8,5)...C(2,1)*C(8,4)...C(2,2)*C(8,3)
........C(3,0)*C(7,5)...C(3,1)*C(7,4)...C(3,2)*C(7,3)...C(3,3)*C(7,2)
...C(4,0)*C(6,5)...C(4,1)*C(6,4)...C(4,2)*C(6,3)...C(4,3)*C(8,2)...C(4,4)*C(6,1)
C(5,0)*C(5,5)...C(5,1)*C(5,4)...C(5,2)*C(5,3)...C(5,3)*C(5,2)...C(5,4)*C(5,1)...C(5,5)*C(5,0)
...C(6,1)*C(4,4)...C(4,1)*C(6,4)...C(4,2)*C(6,3)...C(4,3)*C(8,2)...C(6,5)*C(4,0)
........C(7,2)*C(3,3)...C(7,3)*C(3,2)...C(7,4)*C(3,1)...C(7,5)*C(3,0)
...............C(8,3)*C(2,2)...C(8,4)*C(2,1)...C(8,5)*C(2,0)
......................C(9,4)*C(1,1)...C(9,5)*C(1,0)
.............................C(10,5)*C(0,0)
"m" matching :analogue (permutations with exactly "m" fixed points.
if aaaaabbbbb (a 5 letters b 5 letters) permutations compared aaaaaaaaaa (a 10 times letters) or compared bbbbbbbbbb (b 10 times letters then 252 "5" matching. ("5" matching :analogue(permutations with exactly 5 fixed points.)
If aaaaabbbbb (a 5 letters b 5 letters) permutations compared aaaaabbbbb (a 5 times letters b 5 times letters)then 1 "0" matching),25 "2"matching 100 "4" matching, 100 "6" matching, 25 "8" matching, and 1 "10" matching.(A008459 formatted as a triangular array:6.rows)
If aaaaabbbbb (a 5 letters b 5 letters) permutations compared abbbbbbbbb (a 1 times letters b 9 times letters) or aaaaaaaaab (a 9 times letters b 1 times letters) then 126 "4" and 126 "6" matching.
etc...
matching equivalent "fixpoint"
example:
arrangement relevant!
compared
letters
times
matching:0.....1.....2.....3.....4.....5.....6.....7.....8.....9.....10
compared.
letters..
times....
.a..b
10..0.................................252..............................
.9..1...........................126.........126........................
.8..2......................56.........140..........56..................
.7..3................21.........105.........105..........21............
.6..4..........6...........60.........120..........60..........6.......
.5..5....1...........25.........100.........100..........25...........1
.4..6..........6...........60.........120..........60..........6.......
.3..7................21.........105.........105..........21............
.2..8......................56.........140..........56..................
.1..9...........................126.........126........................
0..10..................................252.............................
matching.0.....1.....2.....3.....4.....5.....6.....7.....8.....9.....10
The Maple code produces
252, 126, 56, 21, 6, 1
126, 140, 105, 60, 25, 6
56, 105, 120, 100, 60, 21
21, 60, 100, 120, 105, 56
6, 25, 60, 105, 140, 126
1, 6, 21, 56, 126, 252
which is the table rotated right by pi/4.
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