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Okay, TIRED poly math geeks gone wild

So, in this entry about finding the formula to determine the total number of possible relationship configurations for any group of n people, blaisepascal observed that the sum we came up with did not consider the case where everyone is involved with everyone else, which is something we had intended to include. The previous equation, therefore, has an off-by-one error. The correct form is:

This is, as many people have observed, essentially the standard "pick r of n permutations" equation, which (had we been thinking along those lines) we likely should've recognized from the start. And, to be fair, one of the more math-geeky among us said something like that early on, but it took much scribbling on many sheets of paper to prove it.


( 13 comments — Leave a comment )
Apr. 9th, 2006 07:30 pm (UTC)
Since 0! == 1, you can simply change the upper limit of the sum to be 'n' and not need the additional +1 (ie nCn = 1).

If you consider the case of masturbation then the lower limit could be 1.

You don't need the restriction k>=2 since you define n>=2 and k ranges from 2 to n (with my modification) it's automatically restricted. Without my change you have the potential for k ranging from 2 to 1 (if n==2) which doesn't make sense.
Apr. 9th, 2006 09:54 pm (UTC)
And this would definetly make a good "most obscure poly shirt EVER" LOL
Apr. 10th, 2006 07:21 am (UTC)
obsure poly shirts
done! www.theinnbetween.net/giftshop.html (http://www.theinnbetween.net/giftshop.html)

Apr. 9th, 2006 11:36 pm (UTC)
If you put this on a T-shirt you could subtitle it "The New Theory of Relativity"
Apr. 10th, 2006 04:49 am (UTC)
I'm a bit rusty - does that include the fact people should have a good relationship with themselves?
Apr. 10th, 2006 12:35 pm (UTC)
No, I don't believe this formula calculates the all important relationship with self. But just add N, and you're there :)
Apr. 10th, 2006 01:35 pm (UTC)
It could be just me, and it's been awhile, but I think your k parameter is set wrong. Otherwise, you have the summation going from K=2 to 1. And that's ...well unusual.

Cute shirt idea!! I'm waiting for the tinkertoy shirt to come out personally. I'm a classics kind of person.

Apr. 10th, 2006 07:54 pm (UTC)
speaking of tinkertoys, I went out and purchased a set of tinkertoys to build a 3D model of The Squiggle. I have to return it and get a bigger set! But it looks cool so far!
Apr. 10th, 2006 01:39 pm (UTC)
When I see things like this, I wish I were math-geeky enough to appreciate the the expression in its native elegant language.

Apr. 10th, 2006 04:26 pm (UTC)
Sounds like a certain geek squad could use a refresher if this was found troublesome to compute. Here's one I encountered just a few days ago:


- ZM
Apr. 26th, 2006 08:38 am (UTC)
Hello! I was pointed to this entry by my partner, and it caught my attention. I have some good news and some bad news (and some sad, geeky news).

The bad news (because I'm a bad-news-first-type-person) is that it seems what you have there is wrong (but feel free to correct me, because I'm really curious about your version of the formula and how it came about).

The good news is that what looks like a better choice for the enumeration formula is even scarier, and probably more t-shirt-worthy, if we can get it to fit.

The sad, geeky news is that when I realised the formula didn't enumerate properly, I sat down with my own wad of paper, went through about 30 sides in the space of two weeks (hey, my Copious Free Time is pretty limited), researched things a bit, and, er, wrote it all up. Yes, I'm sad. You can get the write-up here.
Jul. 28th, 2006 03:26 am (UTC)
...bizarre. Around the same time that you did this, I also did this with one of my sweeties. Because we were very focused at the time on a person's relationship with themselves and getting adequate alone-time in the complexifyin' relationship set, we included each person alone in the equation. When all was said and done, our sum simplified (yay Maple) to 2^n-1.
Jul. 30th, 2006 08:08 pm (UTC)
Re: Serendipity
Yep, the "closed form" Riemann sum simplifies to 2^n-n-1 (if you don't count singletons) or 2^n-1 (if you count singletons but don't count the null case). I personally like the summation form better, but the simplified form is a lot...well, simpler. :)
( 13 comments — Leave a comment )