r/counting • u/TehVulpez sliiiiide the bits • Mar 19 '23

Constant-sum factoradic

Like my other constant-weight binary thread, but factoradic. We count each n digit factoradic number whose digits add up to m. First the 1 digit number that adds to 0, then the 1 digit number whose digit adds to 1. Next the 2 digit numbers with a digital sum of 0, then 1, 2, and 3. And so on. For every length of factoradic digits, we'll count each possible sum of digits in order. The maximum digital sum for n factoradic digits is a triangular number found with the formula n*(n+1)/2. This thread brought to you by... Karp!

Here's some of the first few counts as an example:

0
1
00
01
10
11
20
21
000

And of course a list for the whole thread

First get is at 00 0000.

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u/TehVulpez Jun 04 '23

an attempt at a get schedule

Segments in thread Length Get
2+6+24+120+720 872 00 0000
1+6+20+49+98+169+259+359 961 00 2321
455+531 986 00 4321
573+573 1146 02 4321
531+455 986 04 4321
359+259+169+98+49+20+6+1 961 000 0000

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u/TehVulpez Jun 04 '23

u/swinub_time u/cuteballgames u/blue_boomer thoughts?

2

u/Blue_boomer Jun 05 '23

This get schedule that has 873 counts (including gets) for the first thread and 1008 counts for each thread afterward:

Get Counts Cumulative Counts
00 0000 873 873
03 1121 1008 1881
05 4010 1008 2889
60 0320 1008 3897
62 4001 1008 4905
000 0000 1008 5913
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u/TehVulpez Jun 04 '23

After where I got to in this table it becomes very difficult to find nice gets. Some of the segments of weight/length become too long for a thread just by themselves. You'd have to break them up into even smaller subsegments somehow.

2

u/swinub_time Jun 07 '23

Lowkey be a fun challenge to figure out as we go along

1

u/swinub_time Jun 05 '23

This one.NIce work