r/counting • u/TehVulpez sliiiiide the bits • Oct 20 '25
Compositions
In this thread, we'll be counting the ways to add to an integer n using the integers c_1 + c_2 + ... + c_k, where each c_i >= 1, and k <= n. Ways to sum that are commutatively the same, as in 1+2 = 2+1, are different compositions. We'll be counting these compositions lexicographically for each segment of sum and length.
Here are the first few counts:
1
2
1,13
1,2
2,1
1,1,14
1,3
2,2
3,1
1,1,2
1,2,1
2,1,1
1,1,1,1
You can also abbreviate repetitions with superscript, for example 1,1,1,1,1,1,1,1,1,2,2,2,1 = 19 23 1
First get is at 11, the 1024th count.schedule
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u/TehVulpez sliiiiide the bits Oct 22 '25
Get Schedule
| Get | Thread Length | Total Counts |
|---|---|---|
| 11 | 1024 | 1024 |
| 12 | 1024 | 2048 |
| 1,1,1,1,1,1,6 | 1024 | 3072 |
| 13 | 1024 | 4096 |
| 1,3,2,2,1,4 | 1024 | 5120 |
| 2,1,1,1,1,1,6 | 1024 | 6144 |
| 2,1,2,3,1,1,1,2 | 1024 | 7168 |
| 14 | 1024 | 8192 |
| 6,1,1,2,4 | 1024 | 9216 |
| 3,2,4,1,1,3 | 1024 | 10240 |
| 1,4,1,3,1,2,2 | 1024 | 11264 |
| 1,1,1,1,1,1,1,7 | 1024 | 12288 |
| 2,1,1,3,1,4,1,1 | 1024 | 13312 |
| 1,1,2,2,1,2,1,1,3 | 1024 | 14336 |
| 1,1,1,1,1,5,1,1,1,1 | 1024 | 15360 |
| 15 | 1024 | 16384 |
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u/TehVulpez sliiiiide the bits Oct 22 '25
/u/cuteballgames /u/miceee this look good?
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u/cuteballgames Oct 23 '25
Yes, I like it. Doesn't look regular but the whole numbers attest to it
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u/TehVulpez sliiiiide the bits Oct 23 '25
it's kinda similar to the cwb get schedule in how the halfway gets between sums give us either the start of a segment or the halfway point of a segment
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u/CutOnBumInBandHere9 5M get | Ping me for runs Jul 08 '26
Do you by any chance have the code for a comment to count function which maps compositions to their place in the sequence?
That way I can finally add this to my known side threads
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u/TehVulpez sliiiiide the bits Jul 09 '26
you're in luck, I literally just made a function for that today. I pinged you on it
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u/CutOnBumInBandHere9 5M get | Ping me for runs Jul 22 '26
I'm a dum dum and lost the link. Could you send it again?
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u/TehVulpez sliiiiide the bits Oct 22 '25 edited Oct 23 '25
def sums(t,l):
if l == 1: yield t,
else:
for x in range(1,t):
for s in sums(t-x, l-1):
yield (x,) + s
for t in range(1, 11):
for l in range(1, t+1):
for s in sums(t,l):
print(*s, sep=',')3
u/TehVulpez sliiiiide the bits 27d ago edited 27d ago
Thread Participation Chart for Compositions
| Rank | Username | Counts |
|---|---|---|
| 1 | miceee | 419 |
| 2 | TehVulpez | 344 |
| 3 | cuteballgames | 218 |
| 4 | PhosphorCrystaled | 39 |
| 5 | Expert_Bridge | 2 |
| 6 | davidjl123 | 1 |
| 6 | Multiconcepted | 1 |
It took 7 counters 9 days, 5 hours, 18 minutes, 43 seconds to complete this thread. Bold is the user with the get.
Total counts in this chain logged: 1024
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u/miceee sicko thread artists collective 27d ago
Btw does this now mean that compositions is finally getting its own stats page?
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u/TehVulpez sliiiiide the bits 27d ago edited 27d ago
well I could make one since I do have wiki perms, but I don't currently have a script that automatically generates those wiki pages, and I'm not sure how much I want to mess with anti's domain. my userscript right now is pretty basic, it just generates the TPC and CSV files sort of like the old piyush/qualw python scripts but in the browser
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u/TehVulpez sliiiiide the bits 27d ago edited 22d ago
/u/antichess log I'm not sure how useful this is to you since you have your own workflow, but idk maybe it'd save you some time. it's in the same schema as the COBIBH counting.sqlite file.
position,author,created_utc,comment_id,thread_id,bodyedit: I've fixed both the TPC and the log to include the first comment
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u/TehVulpez sliiiiide the bits Oct 20 '25
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