A169584 - OEIS

%I #12 Oct 10 2024 05:10:56

%S 1,10,76,543,3904,29034,225753

%N The number of 2-noncrossing permutations of n elements.

%C 2nd column of table on p.4 of Burrill, Mishna, and Post. Table 2. Column 1 is the Catalan numbers A000108. The number of permutations of S_n with crossing number k. A crossing number of 1 is equivalent to non-crossing.

%H Sophie Burrill, Marni Mishna and Jacob Post, <a href="http://arxiv.org/abs/0912.0239">On k-crossings and k-nestings of permutations</a>, arXiv:0912.0239 [math.CO], 2009.

%H William Y. C. Chen, Eva Y. P. Deng, Rosena R. X. Du, Richard P. Stanley, and Catherine H. Yan, <a href="https://doi.org/10.1090/S0002-9947-06-04210-3">Crossings and nestings of matchings and partitions</a>, Trans. Amer. Math. Soc., 359(4):1555-1575 (electronic), 2007.

%H Sylvie Corteel, <a href="https://doi.org/10.1016/j.aam.2006.01.006">Crossings and alignments of permutations</a>, Adv. Appl. Math 38 (2007) 149-163.

%H Anna de Mier, <a href="https://arxiv.org/abs/math/0602195">k-Noncrossing and k-nonnesting graphs and fillings of Ferrers diagrams</a>, arXiv:math/0602195 [math.CO], 2006.

%H Anna de Mier, <a href="https://doi.org/10.1007/s00493-007-2297-2">k-noncrossing and k-nonnesting graphs and fillings of Ferrers diagrams</a>, Combinatorica, 27(6), 699-720, 2007.

%Y Cf. A000108.

%K nonn,more

%O 3,2

%A _Jonathan Vos Post_, Dec 02 2009