A192865 Number of set partitions of {1,...,n} that avoid enhanced 5-crossings (or 5-nestings).
1, 1, 2, 5, 15, 52, 203, 877, 4140, 21146, 115945, 678012, 4205209, 27531954, 189486817, 1365888674, 10278272450, 80503198320, 654544093035, 5511256984436, 47950929125540
Offset: 0
Keywords
Examples
There are 21147 partitions of 9 elements, but a(9)=21146 because the partition {1,9}{2,8}{3,7}{4, 6}{5} has an enhanced 5-nesting.
Links
- M. Bousquet-Mélou and G. Xin, On partitions avoiding 3-crossings, math.CO/0506551.
- Sophie Burrill, Sergi Elizalde, Marni Mishna and Lily Yen, A generating tree approach to k-nonnesting partitions and permutations, arXiv preprint arXiv:1108.5615, 2011
- W. Chen, E. Deng, R. Du, R. P. Stanley, and C. Yan, Crossings and nestings of matchings and partitions, math.CO/0501230
- Juan B. Gil, 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