Compositions

[u/TehVulpez]

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
1,1

3
1,2
2,1
1,1,1

4
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

[u/TehVulpez]

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

[u/TehVulpez → u/TehVulpez]

/u/cuteballgames /u/miceee this look good?

[u/cuteballgames → u/TehVulpez]

Yes, I like it. Doesn't look regular but the whole numbers attest to it

[u/TehVulpez → u/cuteballgames]

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

[u/CutOnBumInBandHere9 → u/TehVulpez]

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

[u/TehVulpez → u/CutOnBumInBandHere9]

you're in luck, I literally just made a function for that today. I pinged you on it

[u/CutOnBumInBandHere9 → u/TehVulpez]

I'm a dum dum and lost the link. Could you send it again? 

[u/TehVulpez → u/CutOnBumInBandHere9]

you got it

[u/cuteballgames → u/TehVulpez]

The Vulpine threads are so beautiful

[u/miceee → u/TehVulpez]

Yeah!

[u/TehVulpez]

1

[u/cuteballgames → u/TehVulpez]

2

[u/TehVulpez → u/cuteballgames]

1+1

[u/cuteballgames → u/TehVulpez]

3

[u/TehVulpez → u/cuteballgames]

1+2

[u/cuteballgames → u/TehVulpez]

2,1

tfw i establish the precedent of plus-comma equivalency

[u/TehVulpez → u/cuteballgames]

1,1,1

thread just started and already there's a format war smh nvm fuck pluses, commas all the way

[u/cuteballgames → u/TehVulpez]

4

my mind is contagious

[u/TehVulpez → u/cuteballgames]

1,3

if we make a partitions thread though I'll insist on pluses for that one

[u/cuteballgames → u/TehVulpez]

2,2

why's that

[u/TehVulpez]

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

[u/miceee → u/TehVulpez]

Btw does this now mean that compositions is finally getting its own stats page?

[u/TehVulpez → u/miceee]

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

[u/miceee → u/TehVulpez]

Ohh okay😔 lets wait for anti then

[u/TehVulpez → u/TehVulpez]

/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,body

edit: I've fixed both the TPC and the log to include the first comment

[u/TehVulpez]

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=',')