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a(n) is the lexicographically earliest minimal superpermutation on n symbols, where the symbols are {1, 2, ..., n}, with 1 <= n <= 9.
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%I #29 Sep 26 2024 09:44:28

%S 1,121,123121321,123412314231243121342132413214321,

%T 123451234152341253412354123145213425134215342135421345214352145321452314253142351423154231245312435124315243125432154325143254132451324153241352413254312

%N a(n) is the lexicographically earliest minimal superpermutation on n symbols, where the symbols are {1, 2, ..., n}, with 1 <= n <= 9.

%C Please refer to A332089 (the main entry, where symbols in each superpermutation are individually listed) for more information.

%C In this sequence superpermutations are encoded by concatenating the symbols in a single word. Such encoding ensures unambiguous representation only up to n = 9.

%H Michael Engen and Vincent Vatter, <a href="https://doi.org/10.1080/00029890.2021.1835384">Containing All Permutations</a>, The American Mathematical Monthly, 128 (1), 2021, pp. 4-24 (<a href="https://doi.org/10.48550/arXiv.1810.08252">preprint version</a>).

%H James Grime and Brady Haran, <a href="https://www.youtube.com/watch?v=wJGE4aEWc28">Superpermutations</a>, Numberphile video, 2018.

%H Nathaniel Johnston, <a href="https://doi.org/10.1016/j.disc.2013.03.024">Non-uniqueness of minimal superpermutations</a>, Discrete Mathematics, Vol. 313, Issue 14, 2013, pp. 1553-1557 (<a href="https://doi.org/10.48550/arXiv.1303.4150">preprint version</a>).

%H Nathaniel Johnston, <a href="https://njohnston.ca/2014/08/all-minimal-superpermutations-on-five-symbols-have-been-found/">All Minimal Superpermutations on Five Symbols Have Been Found</a>, 2014.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Superpermutation">Superpermutation</a>.

%Y Cf. A180632, A332089, A332090, A341300, A376269.

%K nonn,hard,fini

%O 1,2

%A _Paolo Xausa_, Sep 20 2024