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Number of set partitions of {1, ..., n} that avoid enhanced 4-crossings (or enhanced 4-nestings)
3

%I #24 May 24 2020 00:10:17

%S 1,1,2,5,15,52,203,876,4120,20883,113034,648410,3917021,24785452,

%T 163525976,1120523114,7947399981,58172358642,438300848329,

%U 3391585460591,26898763482122

%N Number of set partitions of {1, ..., n} that avoid enhanced 4-crossings (or enhanced 4-nestings)

%H M. Bousquet-Mélou and G. Xin, <a href="http://arXiv.org/abs/math.CO/0506551">On partitions avoiding 3-crossings</a>, math.CO/0506551.

%H Sophie Burrill, Sergi Elizalde, Marni Mishna and Lily Yen, <a href="http://arxiv.org/abs/1108.5615">A generating tree approach to k-nonnesting partitions and permutations</a>, arXiv preprint arXiv:1108.5615, 2011

%H W. Chen, E. Deng, R. Du, R. P. Stanley, and C. Yan, <a href="http://arXiv.org/abs/math.CO/0501230">Crossings and nestings of matchings and partitions</a>, math.CO/0501230

%H Juan B. Gil, Jordan O. Tirrell, <a href="https://arxiv.org/abs/1806.09065">A simple bijection for classical and enhanced k-noncrossing partitions</a>, arXiv:1806.09065 [math.CO], 2018. Also Discrete Mathematics (2019) Article 111705. doi:10.1016/j.disc.2019.111705

%e 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.

%Y Cf. A000110, A108307.

%K nonn

%O 0,3

%A _Marni Mishna_, Jul 11 2011