A218970 Number of connected cyclic conjugacy classes of subgroups of the symmetric group.
1, 1, 1, 1, 2, 1, 4, 1, 5, 3, 8, 2, 14, 3, 17, 11, 24, 10, 40, 16, 53, 35, 71, 43, 112, 68, 144, 112, 203, 152, 301, 219, 393, 342, 540, 474, 770, 661, 1022, 967, 1397, 1313, 1928, 1821, 2565, 2564, 3439, 3445, 4676, 4687, 6186, 6406, 8215, 8543, 10974, 11435
Offset: 0
Keywords
Examples
From _Gus Wiseman_, Dec 03 2018: (Start) The a(12) = 14 connected integer partitions of 12: (12) (6,6) (4,4,4) (3,3,3,3) (4,2,2,2,2) (2,2,2,2,2,2) (8,4) (6,3,3) (4,4,2,2) (9,3) (6,4,2) (6,2,2,2) (10,2) (8,2,2) (End)
Links
- Liam Naughton and Goetz Pfeiffer, Integer sequences realized by the subgroup pattern of the symmetric group, arXiv:1211.1911 [math.GR], 2012-2013.
- Liam Naughton, CountingSubgroups.g
- Liam Naughton and Goetz Pfeiffer, Tomlib, The GAP table of marks library
Crossrefs
Programs
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Mathematica
zsm[s_]:=With[{c=Select[Tuples[Range[Length[s]],2],And[Less@@#,GCD@@s[[#]]]>1&]},If[c=={},s,zsm[Sort[Append[Delete[s,List/@c[[1]]],LCM@@s[[c[[1]]]]]]]]]; Table[Length[Select[IntegerPartitions[n],Length[zsm[#]]==1&]],{n,10}]
Formula
For n > 1, a(n) = A304716(n) - 1. - Gus Wiseman, Dec 03 2018
Extensions
More terms from Gus Wiseman, Dec 03 2018
Comments