A192855 Number of set partitions of {1, ..., n} that avoid enhanced 4-crossings (or enhanced 4-nestings).
1, 1, 2, 5, 15, 52, 203, 876, 4120, 20883, 113034, 648410, 3917021, 24785452, 163525976, 1120523114, 7947399981, 58172358642, 438300848329, 3391585460591, 26898763482122
Offset: 0
Examples
There are 877 partitions of 7 elements, but a(7)=51 because the partition {1,7}{2,6}{3,5}{4} has an enhanced 4-nesting.
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], 2011-2014.
- W. Chen, E. Deng, R. Du, R. P. 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], 2018-2023. Also Discrete Mathematics (2019) Article 111705, doi:10.1016/j.disc.2019.111705.