A192126 Number of set partitions of {1, ..., n} that avoid 5-nestings.
1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115974, 678530, 4212654, 27627153, 190624976, 1378972826, 10425400681, 82139435907, 672674215928, 5712423473216, 50193986895328, 455436027242590, 4259359394306331
Offset: 0
Examples
There are 115975 partitions of 10 elements, but a(10)=115974 because the partition {1,10}{2,9}{3,8}{4,7}{5,6} has a 5-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.
- 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.
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