$11^{3}_{12}$ - Minimal pinning sets
Pinning sets for 11^3_12 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^3_12 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 64
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: 2.83846
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, 2, 4, 6, 11}
5
[2, 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
5
1
0
0
2.0
6
0
0
6
2.39
7
0
0
15
2.67
8
0
0
20
2.88
9
0
0
15
3.04
10
0
0
6
3.17
11
0
0
1
3.27
Total
1
0
63
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 3, 4, 4, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,3,3,4],[0,5,5,0],[0,6,1,1],[1,6,6,7],[2,7,8,2],[3,8,4,4],[4,8,8,5],[5,7,7,6]]
PD code (use to draw this multiloop with SnapPy): [[3,10,4,1],[2,14,3,11],[9,4,10,5],[1,12,2,11],[13,18,14,15],[5,8,6,9],[12,16,13,15],[7,17,8,18],[6,17,7,16]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (7,2,-8,-3)(3,6,-4,-7)(1,8,-2,-9)(10,11,-1,-12)(12,9,-13,-10)(15,4,-16,-5)(5,16,-6,-17)(14,17,-11,-18)(18,13,-15,-14)
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,-9,12)(-2,7,-4,15,13,9)(-3,-7)(-5,-17,14,-15)(-6,3,-8,1,11,17)(-10,-12)(-11,10,-13,18)(-14,-18)(-16,5)(2,8)(4,6,16)
Multiloop annotated with half-edges
11^3_12 annotated with half-edges