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

Offset

0,3

Links

Table of n, a(n) for n=0..20.

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.

Example

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.

Crossrefs

Sequence in context: A287668 A099262 A141081 * A229224 A343668 A276724

Adjacent sequences: A108302 A108303 A108304 * A108306 A108307 A108308

Keyword

easy,nonn,more

Author

Mireille Bousquet-Mélou, Jun 29 2005

Status

approved