Regaurding the mathematical effects of quadrants on the total number of posible ships in homestuck.

Hello FRAF.. i want to do some maths.

The total number of possible ships in a work is reletively simple to calculate. Is what i first thought... and then i realised i was wrong so we get skip straight to the maths.

I thought it was pretty simple, every purmutaion of every pair of characters so C^2 with C being characters and 2 representing relationships with two characters. it was only later i realised its actually not so simple.

see C^2 represents every permutation of a caracter and another character. however this formula ends up counting some pairs twice as it considers two characters in a seperate order a different ship. (e.g. dad,mom and mom,dad are counted seperately) so i looked into it and found i should have been calculating for every combination!

so lets look at the combination formula. first off we have to consider are we doing repetition? Flip no! i glanced over the explaination for repetition and it was freaking scary! so im very sorry mirrorshippers but i cannot include you in my calculations. Now thats decided lets get down to brass tacks.

ok basically we start with number of every pairing of two characters. with C for caractrs and R for pairs. (C!/(C-R)!) this gives us every combination of two characters in every order that two characters can be. then we reduce it by every pair that is a repeat. we do this by multiplying by (1/R!)

so this brings the formula for the number of ships in any given fandom to ((c!/(c-r)!)*(1/r!)) with c being the number of shipped characters and r being the number of characters in every ship (it is an important tool for later). p.s. id embed imaged with drawn up formulas but imlazzyyyyy.

so now we have a formula we just gotta plug numbers in right? No! of course you didnt think that, you as a good homestuck fan know about the quadrants, alternative systems of romance that our caracters can participate in! so lets get to quadrants shall we?

well quadrants arre pretty easy actually. if our formula calculates every possible ship on a shipping grid then we simply have to multiply our formula by four! for our four shpping grids... oh yeah auspicticism.

ok so lets start with the simple part. 3((c!/(c-2)!)*(1/2!)) represents every matesprit, kismesis, and moirail pairing that can exist within a certain set of characters(C). we are going to add to that the auspicticism formula with new special variable A (which stands for awfulness) taking the place of r. the auspicsticism formula is as such a((c!/(c-a)!)*(1/a!)) Now it is mostly the same with our formula actually being able to compute the value of three in the place of a. However there is in fact a stray a at the very start that i had to add to account for the fact that one member of the ashen ship is the auspictice. basically for every combination of three characters i multipy by the number of characters to represent a situation where each one is the auspictice. This is incredibly stupid and made my math wrong twice.

now we have all we need. thhe number of total ships in homestuck can be calculated by the equation: 3((c!/(c-r)!)*(1/r!))+a((c!/(c-a)!)*(1/a!)) trust me it looks more complicated all typed out like that. compare this to our first equation and substitute the r and a variables as 2 and 3 respectively then you find that the quadrants create 2((c!/(c-2)!)*(1/2!))+3((c!/(c-3)!)*(1/3!)) more ships than a regular fandom does!

also if you take the total ships and substite the values plus substituting the total shippable caracters that i approximated to be 83 you get this:
3((82!/(82-2)!)*(1/2!))+3((82!/(82-3)!)*(1/3!))
which im not going to try typing into a calculator cause i know they error at 70! so there you have it. i did maths. i ad to learn what combinatorics was for this post. There is probably a billion spelling errors and at least two errors in my explaination so feel free to comment corrections and reactions. i will be back with a mirrorshipping addendum (for you eridan<3eridan lovers and karkat c3< karkat c3< jade enjoyers)