$12^{2}_{272}$ - Minimal pinning sets
Pinning sets for 12^2_272 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_272 Pinning data
Pinning number of this multiloop: 6
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: 2.85421
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, 3, 5, 7, 11}
6
[2, 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
6
1
0
0
2.0
7
0
0
6
2.38
8
0
0
15
2.67
9
0
0
20
2.89
10
0
0
15
3.07
11
0
0
6
3.21
12
0
0
1
3.33
Total
1
0
63
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 3, 4, 5, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,5,0],[0,6,7,7],[0,8,8,9],[1,9,9,5],[1,4,6,6],[2,5,5,9],[2,8,8,2],[3,7,7,3],[3,6,4,4]]
PD code (use to draw this multiloop with SnapPy): [[16,5,1,6],[6,15,7,16],[9,4,10,5],[1,12,2,13],[14,20,15,17],[7,20,8,19],[8,18,9,19],[3,10,4,11],[11,2,12,3],[13,18,14,17]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,16,-10,-1)(7,2,-8,-3)(14,3,-15,-4)(1,8,-2,-9)(15,10,-16,-11)(4,13,-5,-14)(6,17,-7,-18)(18,5,-19,-6)(12,19,-13,-20)(20,11,-17,-12)
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)(-19,19)(-20,20)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,-9)(-2,7,17,11,-16,9)(-3,14,-5,18,-7)(-4,-14)(-6,-18)(-8,1,-10,15,3)(-11,20,-13,4,-15)(-12,-20)(-17,6,-19,12)(2,8)(5,13,19)(10,16)
Multiloop annotated with half-edges
12^2_272 annotated with half-edges