login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A324166 Number of totally crossing set partitions of {1,...,n}. 15
1, 1, 1, 1, 2, 6, 18, 57, 207, 842, 3673, 17062, 84897 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

A set partition is totally crossing if every pair of distinct blocks is of the form {{...x...y...}, {...z...t...}} for some x < z < y < t or z < x < t < y.

LINKS

Table of n, a(n) for n=0..12.

EXAMPLE

The a(6) = 18 totally crossing set partitions:

  {{1,2,3,4,5,6}}

  {{1,4,6},{2,3,5}}

  {{1,4,5},{2,3,6}}

  {{1,3,6},{2,4,5}}

  {{1,3,5},{2,4,6}}

  {{1,3,4},{2,5,6}}

  {{1,2,5},{3,4,6}}

  {{1,2,4},{3,5,6}}

  {{4,6},{1,2,3,5}}

  {{3,6},{1,2,4,5}}

  {{3,5},{1,2,4,6}}

  {{2,6},{1,3,4,5}}

  {{2,5},{1,3,4,6}}

  {{2,4},{1,3,5,6}}

  {{1,5},{2,3,4,6}}

  {{1,4},{2,3,5,6}}

  {{1,3},{2,4,5,6}}

  {{1,4},{2,5},{3,6}}

MATHEMATICA

nn=6;

nonXQ[stn_]:=!MatchQ[stn, {___, {___, x_, ___, y_, ___}, ___, {___, z_, ___, t_, ___}, ___}/; x<z<y<t||z<x<t<y];

stableSets[u_, Q_]:=If[Length[u]===0, {{}}, With[{w=First[u]}, Join[stableSets[DeleteCases[u, w], Q], Prepend[#, w]&/@stableSets[DeleteCases[u, r_/; r===w||Q[r, w]||Q[w, r]], Q]]]];

Table[Length[Select[stableSets[Subsets[Range[n], {1, n}], Intersection[#1, #2]!={}||nonXQ[{#1, #2}]&], Union@@#==Range[n]&]], {n, 0, nn}]

CROSSREFS

Cf. A000108 (non-crossing partitions), A000110, A000296, A002662, A016098 (crossing partitions), A054726, A099947 (topologically connected partitions), A305854, A306006, A306418, A306438, A319752.

Cf. A324170, A324171, A324172, A324173.

Sequence in context: A273203 A148458 A148459 * A307755 A304200 A081057

Adjacent sequences:  A324163 A324164 A324165 * A324167 A324168 A324169

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Feb 17 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 10 08:09 EDT 2021. Contains 342845 sequences. (Running on oeis4.)