Formula sought (enumerative combinatorics)

28/06/2008 - 16:21 von Adem24 | Report spam
Formula sought

For the below input parameters v and k, v>=k,
what would be the equation that gives b ?

FYI: these parameters and results are integer values
from the field of enumerative combinatorics.
The b below is the result of a complete enumeration
for the given v,k.
What is needed is to know in advance how much b will be
for the given v,k without enumerating the whole set.
Can one formulate an equation for this?

v k b
1 1 1
2 1 2
3 1 3

2 2 1
3 2 4
4 2 9
5 2 16

3 3 1
4 3 9
5 3 28
6 3 65
7 3 126

4 4 1
5 4 21
6 4 90
7 4 268
8 4 640
9 4 1314

5 5 1
6 5 52
7 5 298
8 5 1123
9 5 3278
10 5 7995
11 5 17104

6 6 1
7 6 136
8 6 1016
9 6 4783
10 6 16941
11 6 48895
12 6 121171
13 6 267369

7 7 1
8 7 379
9 7 3575
10 7 20720
11 7 88393
12 7 300683
13 7 861325
14 7 2160889
15 7 4884281

8 8 1
9 8 1126
10 8 13023
11 8 91412
12 8 465938
13 8 1860121
14 8 6144894
15 8 17505487
16 8 44343520
17 8 102177477

...
 

Lesen sie die antworten

#1 Mariano Suárez-Alvarez
28/06/2008 - 20:29 | Warnen spam
On Jun 28, 11:21 am, "Adem24" wrote:
Formula sought

For the below input parameters v and k, v>=k,
what would be the equation that gives b ?

FYI: these parameters and results are integer values
from the field of enumerative combinatorics.
The b below is the result of a complete enumeration
for the given v,k.
What is needed is to know in advance how much b will be
for the given v,k without enumerating the whole set.
Can one formulate an equation for this?



Why don't you tell us *what* you are enumerating?
The chances of coming up with something sensible
will then be enormously higher...

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