$12^{1}_{318}$ - Minimal pinning sets
Pinning sets for 12^1_318 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_318 Pinning data
Pinning number of this loop: 7
Total number of pinning sets: 32
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: 2.80821
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, 4, 7, 8, 9, 11}
7
[2, 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
7
1
0
0
2.0
8
0
0
5
2.4
9
0
0
10
2.71
10
0
0
10
2.96
11
0
0
5
3.16
12
0
0
1
3.33
Total
1
0
31
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 7, 8]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,2],[0,3,3,0],[0,4,4,0],[1,5,6,1],[2,7,8,2],[3,8,8,6],[3,5,9,9],[4,9,9,8],[4,7,5,5],[6,7,7,6]]
PD code (use to draw this loop with SnapPy): [[7,20,8,1],[19,6,20,7],[8,2,9,1],[5,18,6,19],[2,10,3,9],[4,13,5,14],[17,12,18,13],[10,16,11,15],[3,15,4,14],[11,16,12,17]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (17,4,-18,-5)(7,20,-8,-1)(15,10,-16,-11)(2,11,-3,-12)(12,1,-13,-2)(13,8,-14,-9)(9,14,-10,-15)(3,16,-4,-17)(5,18,-6,-19)(19,6,-20,-7)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,12,-3,-17,-5,-19,-7)(-2,-12)(-4,17)(-6,19)(-8,13,1)(-9,-15,-11,2,-13)(-10,15)(-14,9)(-16,3,11)(-18,5)(-20,7)(4,16,10,14,8,20,6,18)
Loop annotated with half-edges
12^1_318 annotated with half-edges