A108305 Number of set partitions of {1, ..., n} that avoid 4-crossings.

1, 1, 2, 5, 15, 52, 203, 877, 4139, 21119, 115495, 671969, 4132936, 26723063, 180775027, 1274056792, 9320514343, 70548979894, 550945607475, 4427978077331, 36544023687590, 309088822019071

Offset: 0

Author

Mireille Bousquet-Mélou, Jun 29 2005

Keywords

• nonn
• more

Examples

			There are 4140 partitions of 8 elements, but a(8) = 4139 because the partition (1,5)(2,6)(3,7)(4,8) has a 4-crossing.
		

Links

• M. Bousquet-Mélou and G. Xin, On partitions avoiding 3-crossings, arXiv:math/0506551 [math.CO], 2005-2006.
• Sophie Burrill, Sergi Elizalde, Marni Mishna and Lily Yen, A generating tree approach to k-nonnesting partitions and permutations, arXiv preprint arXiv:1108.5615 [math.CO], 2011.
• W. Chen, E. Deng, R. Du, R. Stanley, and C. Yan, Crossings and nestings of matchings and partitions, arXiv:math/0501230 [math.CO], 2005.
• Juan B. Gil and Jordan O. Tirrell, A simple bijection for classical and enhanced k-noncrossing partitions, arXiv:1806.09065 [math.CO], 2018. Also Discrete Mathematics (2019) Article 111705. doi:10.1016/j.disc.2019.111705
• M. Mishna and L. Yen, Set partitions with no k-nesting, arXiv:1106.5036 [math.CO], 2011-2012.

Crossrefs

Cf. A108304 (k = 3), (this: k = 4), A192126 (k = 5), A192127 (k = 6), A192128 (k = 7).

Cf. A192855.

Extensions

One more value from Burrill et al (2011). - R. J. Mathar, May 25 2025