A108305
Number of set partitions of {1, ..., n} that avoid 4-crossings.
Original entry on oeis.org
1, 1, 2, 5, 15, 52, 203, 877, 4139, 21119, 115495, 671969, 4132936, 26723063, 180775027, 1274056792, 9320514343, 70548979894, 550945607475, 4427978077331, 36544023687590, 309088822019071
Offset: 0
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.
- 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.
One more value from Burrill et al (2011). -
R. J. Mathar, May 25 2025
A366776
Number of 2-distant 5-noncrossing partitions of {1,...,n}.
Original entry on oeis.org
1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678569, 4213546, 27642948, 190866373, 1382340849, 10469739750, 82701857286, 679644668584, 5797647603036, 51228938289039, 467980667203765
Offset: 0
There are 678570 partitions of 11 elements, but a(11)=678569 because the partition (1,7)(2,8)(3,9)(4,10)(5,11)(6) has a 2-distant 5-crossing.
- Juan B. Gil and Jordan O. Tirrell, A simple bijection for enhanced, classical, and 2-distant k-noncrossing partitions, Discrete Math. 343 (2020), no. 6, 111705, 5 pp.
A192127
Number of set partitions of {1, ..., n} that avoid 6-nestings.
Original entry on oeis.org
1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213596, 27644383, 190897649, 1382919174, 10479355676, 82850735298, 681840170501, 5828967784989, 51665915664913, 473990899143781, 4493642492511044, 43959218211619150
Offset: 0
There are 4213597 partitions of 12 elements, but a(12)=4213597 because the partition {1,12}{2,11}{3,10}{4,9}{5,8}{6,7} has a 6-nesting.
- 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.
- M. Mishna and L. Yen, Set partitions with no k-nesting, arXiv:1106.5036 [math.CO], 2011-2012.
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