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Stack-sortable permutation - Revision history
2026-04-11T00:13:57Z
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218.87.90.250: /* Sorting with a stack */
2013-11-02T07:03:12Z
<p><span class="autocomment">Sorting with a stack</span></p>
<p><b>New page</b></p><div>This honeycomb is one of [[Uniform_polyzetton#Regular_and_uniform_honeycombs|29 unique uniform honeycombs]]<ref>{{mathworld | urlname = Necklace | title = Necklace}}, [http://oeis.org/A000029 A000029] 30-1 cases, skipping one with zero marks</ref> constructed by <br />
the <math>{\tilde{A}}_7</math> [[Coxeter group]], grouped by their extended symmetry of rings within the [[regular octagon]] diagram:<br />
<br />
{|class=wikitable<br />
!Octagon<BR>symmetry<br />
![[Coxeter notation|Extended<BR>symmetry]]<br />
!Extended<BR>diagram<br />
!Extended<BR>order<br />
!Honeycombs<br />
|- align=center<br />
!a1<br />
![3<sup>[8]</sup>]<br />
|{{CDD|node|split1|nodes|3ab|nodes|3ab|nodes|split2|node}}<br />
|×1<br />
|<br />
{{CDD|node_1|split1|nodes_10lur|3ab|nodes|3ab|nodes_10lru|split2|node}}<br />
{{CDD|node_1|split1|nodes_10lur|3ab|nodes|3ab|nodes|split2|node_1}}<br />
{{CDD|node_1|split1|nodes_10lur|3ab|nodes_10lr|3ab|nodes|split2|node_1}}<br />
{{CDD|node_1|split1|nodes_10lur|3ab|nodes|3ab|nodes_11|split2|node}}<br />
{{CDD|node_1|split1|nodes_10lur|3ab|nodes_10lr|3ab|nodes_11|split2|node}}<br />
|- align=center<br />
!d2<br />
!<[3<sup>[8]</sup>]><br />
|{{CDD|node_c1|split1|nodeab_c2|3ab|nodeab_c3|3ab|nodeab_c4|split2|node_c5}}<br />
|×2<br />
|<br />
{{CDD|node|split1|nodes_11|3ab|nodes|3ab|nodes|split2|node}}<br />
{{CDD|node|split1|nodes|3ab|nodes_11|3ab|nodes|split2|node}}<br />
{{CDD|node|split1|nodes_11|3ab|nodes_11|3ab|nodes|split2|node}}<br />
{{CDD|node_1|split1|nodes|3ab|nodes|3ab|nodes|split2|node}}<sub>[[7-simplex honeycomb|1]]</sub><br />
{{CDD|node_1|split1|nodes_11|3ab|nodes|3ab|nodes|split2|node}}<br />
{{CDD|node_1|split1|nodes|3ab|nodes_11|3ab|nodes|split2|node}} <br />
{{CDD|node_1|split1|nodes|3ab|nodes|3ab|nodes_11|split2|node}} <br />
<br />
{{CDD|node_1|split1|nodes_11|3ab|nodes_11|3ab|nodes|split2|node}}<br />
{{CDD|node_1|split1|nodes_11|3ab|nodes|3ab|nodes_11|split2|node}}<br />
{{CDD|node_1|split1|nodes|3ab|nodes_11|3ab|nodes_11|split2|node}}<br />
{{CDD|node_1|split1|nodes_11|3ab|nodes_11|3ab|nodes_11|split2|node}}<br />
{{CDD|node_1|split1|nodes_11|3ab|nodes|3ab|nodes|split2|node_1}}<br />
{{CDD|node_1|split1|nodes_11|3ab|nodes_11|3ab|nodes|split2|node_1}}<br />
|- align=center<br />
!p2<br />
!<nowiki>[[</nowiki>3<sup>[8]</sup>]]<br />
|{{CDD|branch_c1|3ab|nodeab_c2|3ab|nodeab_c3|3ab|branch_c4}}<br />
|×2<br />
|<br />
{{CDD|branch_11|3ab|nodes|3ab|nodes|3ab|branch}} <sub>[[Truncated 7-simplex honeycomb|2]]</sub><br />
{{CDD|branch|3ab|nodes_11|3ab|nodes|3ab|branch}} <br />
{{CDD|branch_11|3ab|nodes_11|3ab|nodes|3ab|branch}} <br />
{{CDD|branch_11|3ab|nodes|3ab|nodes_11|3ab|branch}} <br />
{{CDD|branch_11|3ab|nodes_11|3ab|nodes_11|3ab|branch}} <br />
|- align=center<br />
!d4<br />
!<2[3<sup>[8]</sup>]><br />
|{{CDD|node_c1|split1|nodeab_c2|3ab|nodeab_c3|3ab|nodeab_c2|split2|node_c1}}<br />
|×4<br />
|<br />
{{CDD|node_1|split1|nodes|3ab|nodes|3ab|nodes|split2|node_1}}<br />
{{CDD|node|split1|nodes_11|3ab|nodes_11|3ab|nodes_11|split2|node}}<br />
|- align=center<br />
!p4<br />
!<nowiki>[2[</nowiki>3<sup>[8]</sup>]]<br />
|{{CDD|branch_c1|3ab|nodeab_c2|3ab|nodeab_c2|3ab|branch_c1}}<br />
|×4<br />
|<br />
{{CDD|branch_11|3ab|nodes|3ab|nodes|3ab|branch_11}} <br />
{{CDD|branch|3ab|nodes_11|3ab|nodes_11|3ab|branch}} <br />
|- align=center<br />
!d8<br />
![4[3<sup>[8]</sup>]]<br />
|{{CDD|node_c1|split1|nodeab_c2|3ab|nodeab_c1|3ab|nodeab_c2|split2|node_c1}}<br />
|×8<br />
|{{CDD|node_1|split1|nodes|3ab|nodes_11|3ab|nodes|split2|node_1}}<br />
|- align=center<br />
!r16<br />
![8[3<sup>[8]</sup>]]<br />
|{{CDD|node_c1|split1|nodeab_c1|3ab|nodeab_c1|3ab|nodeab_c1|split2|node_c1}}<br />
|×16<br />
|{{CDD|node_1|split1|nodes_11|3ab|nodes_11|3ab|nodes_11|split2|node_1}}<sub>[[Omnitruncated 7-simplex honeycomb|3]]</sub><br />
|}<noinclude><br />
==References==<br />
{{reflist}}<br />
<br />
[[Category:Encyclopedic content templates]]<br />
</noinclude></div>
218.87.90.250