A376069 a(n) is the lexicographically earliest minimal superpermutation on n symbols, where the symbols are {1, 2, ..., n}, with 1 <= n <= 9.

1, 121, 123121321, 123412314231243121342132413214321, 123451234152341253412354123145213425134215342135421345214352145321452314253142351423154231245312435124315243125432154325143254132451324153241352413254312

Offset: 1

Author

Paolo Xausa, Sep 20 2024

Keywords

• nonn
• hard
• fini

Comments

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

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

Links

• Michael Engen and Vincent Vatter, Containing All Permutations, The American Mathematical Monthly, 128 (1), 2021, pp. 4-24 (preprint version).
• James Grime and Brady Haran, Superpermutations, Numberphile video, 2018.
• Nathaniel Johnston, Non-uniqueness of minimal superpermutations, Discrete Mathematics, Vol. 313, Issue 14, 2013, pp. 1553-1557 (preprint version).
• Nathaniel Johnston, All Minimal Superpermutations on Five Symbols Have Been Found, 2014.
• Wikipedia, Superpermutation.

Crossrefs

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