A376572 - OEIS

%I #12 Sep 29 2024 06:25:08

%S 1,2,1,4,3,2,10,9,8,6,32,33,31,31,26

%N Triangle read by rows: T(n,k) is the frequency of the symbol k in the lexicographically earliest minimal superpermutation on n symbols, where the symbols are {1, 2, ..., n}.

%C Equivalently, T(n,k) is the frequency of k in row n of A332089 (see there for more information).

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

%e Triangle begins:

%e   n\k|  1   2   3   4   5  ...

%e   ----------------------------

%e    1 |  1;

%e    2 |  2,  1;

%e    3 |  4,  3,  2;

%e    4 | 10,  9,  8,  6;

%e    5 | 32, 33, 31, 31, 26;

%e   ...

%e For n = 3, the minimal superpermutation is 123121321; symbol 1 appears 4 times, symbol 2 appears 3 times and symbol 3 appears 2 times.

%Y Cf. A180632 (row sums, for n >= 1), A332089.

%K nonn,tabl,hard,more

%O 1,2

%A _Paolo Xausa_, Sep 28 2024