$11^{2}_{27}$ - Minimal pinning sets
Pinning sets for 11^2_27 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_27 Pinning data
Pinning number of this multiloop: 4
Total number of pinning sets: 128
of which optimal: 1
of which minimal: 1
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.89692
on average over minimal pinning sets: 2.0
on average over optimal pinning sets: 2.0
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 3, 5, 8}
4
[2, 2, 2, 2]
2.00
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
4
1
0
0
2.0
5
0
0
7
2.4
6
0
0
21
2.67
7
0
0
35
2.86
8
0
0
35
3.0
9
0
0
21
3.11
10
0
0
7
3.2
11
0
0
1
3.27
Total
1
0
127
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,3,4,4],[0,5,5,6],[0,6,1,0],[1,7,8,1],[2,8,6,2],[2,5,7,3],[4,6,8,8],[4,7,7,5]]
PD code (use to draw this multiloop with SnapPy): [[10,18,1,11],[11,17,12,16],[4,9,5,10],[17,1,18,2],[12,15,13,16],[8,3,9,4],[5,3,6,2],[6,14,7,15],[13,7,14,8]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (10,3,-1,-4)(6,1,-7,-2)(18,5,-11,-6)(2,7,-3,-8)(14,9,-15,-10)(4,11,-5,-12)(17,12,-18,-13)(13,16,-14,-17)(8,15,-9,-16)
Edge permutation $\epsilon=$ (-1,1)(-2,2)(-3,3)(-4,4)(-5,5)(-6,6)(-7,7)(-8,8)(-9,9)(-10,10)(-11,11)(-12,12)(-13,13)(-14,14)(-15,15)(-16,16)(-17,17)(-18,18)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,6,-11,4)(-2,-8,-16,13,-18,-6)(-3,10,-15,8)(-4,-12,17,-14,-10)(-5,18,12)(-7,2)(-9,14,16)(-13,-17)(1,3,7)(5,11)(9,15)
Multiloop annotated with half-edges
11^2_27 annotated with half-edges