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Are your eyes burning under the glory of OMNISHIPPING??
https://golem.ph.utexas.edu/category/2015/08/a_wrinkle_in_the_mathematical.html
Some terminologies in particular:
• A duad is a 2-element subset of S. Note that there are 6choose2=15 duads.
Duad is what I call a ship.
• A syntheme is a set of 3 duads forming a partition of S. There are also 15 synthemes.
Syntheme is what I call a “picture of three 2-somes”.
• A synthematic total is a set of 5 synthemes partitioning the set of 15 duads. There are 6 synthematic totals.
Synthematic total is what I call a series of shipping pictures.
Edited
Alien and strange, that’s me.
It’s hard to look up the word for something if all you have is the concept. This was a lot of fun to read!
Thank you.
I didn’t know there’s a word for that. I’m, for now, mostly a geometer…
I wrote this during a fever to distract myself from my pain. I would have thought of looking it up to see if there’s a word for it, but I was in a fever.
The three-line pictures are known as a matching, or a 1-factor. A set of 1-factors whose union is the entire graph (the omniship) is known as a factorisation of the graph.
If the question of the exercise is “show that 5 matchings cover the entire omniship,” then since there are 15 lines in the omniship (that’s a fun word to say. Omniship), 5 matchings consisting of three pairs suffice. If the question of the exercise is “show that these are all possible factorisations of the omniship,” then then steps are as follows:
In some matching AJ must ship with Rarity (this is also known as a best or correct shipping). Then, Twi must ship with one of the three remaining Mane 6. There are three free choices; the third ship is then determined.
Identify the next graph by letting AJ ship with RD (this is known as an acceptable shipping). This done, Twi must ship with neither AJ, nor RD, nor the pony she shipped with in the first graph, leaving her two choices. Either is fine.
In the third matching, ship AJ with Twi. Now among the four remaining ponies, there are three possible pairs of matches. It’s longer to argue but it turns out you only have one free choice at this step; some pairings lead to contradictions later (doubling up on an earlier ship).