jm + permutation   4

Sci-Fi Writer Greg Egan and 4chan anon Math Whiz Advance Permutation Problem | Quanta Magazine
On September 16, 2011, an anime fan posted a math question to the online bulletin board 4chan about the cult classic television series 'The Melancholy of Haruhi Suzumiya'. Season one of the show, which involves time travel, had originally aired in non-chronological order, and a re-broadcast and a DVD version had each further rearranged the episodes. Fans were arguing online about the best order to watch the episodes, and the 4chan poster wondered: If viewers wanted to see the series in every possible order, what is the shortest list of episodes they’d have to watch?

In less than an hour, an anonymous person offered an answer — not a complete solution, but a lower bound on the number of episodes required. The argument, which covered series with any number of episodes, showed that for the 14-episode first season of Haruhi, viewers would have to watch at least 93,884,313,611 episodes to see all possible orderings. “Please look over [the proof] for any loopholes I might have missed,” the anonymous poster wrote.

The proof slipped under the radar of the mathematics community for seven years — apparently only one professional mathematician spotted it at the time, and he didn’t check it carefully. But in a plot twist last month, the Australian science fiction novelist Greg Egan proved a new upper bound on the number of episodes required. Egan’s discovery renewed interest in the problem and drew attention to the lower bound posted anonymously in 2011. Both proofs are now being hailed as significant advances on a puzzle mathematicians have been studying for at least 25 years.
mathematics  internet  math  greg-egan  anime  bizarre  4chan  superpermutation  permutation  proofs 
4 weeks ago by jm
Sattolo's algorithm
produces a randomized permutation of a list, with exactly one cycle (which guarantees that we will reach every element of the list even though we’re traversing it in random order)
algorithms  lists  permutation  random  randomization  cycles 
august 2017 by jm
algorithm - Generating shuffled range using a PRNG rather than shuffling - Stack Overflow
some reasonably good answers on using an LFSR or LCG to generate a full-cycle permutation with no repeats
lfsr  lcg  algorithms  permutation  shuffling 
december 2011 by jm
Using a Feistel Network for full-cycle permutation
nice algorithm. requires that the permuted set's size be a power of 2 however - although for smaller sets you can just skip to the next output value, since they're not going to repeat
feistel-network  full-cycle  permutation  shuffling  algorithms 
december 2011 by jm

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