$12^{1}_{129}$ - Minimal pinning sets
Pinning sets for 12^1_129 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_129 Pinning data
Pinning number of this loop: 5
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: 2.90623
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, 5, 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
7
2.38
7
0
0
21
2.65
8
0
0
35
2.86
9
0
0
35
3.02
10
0
0
21
3.14
11
0
0
7
3.25
12
0
0
1
3.33
Total
1
0
127
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 4, 4, 4, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,4,0],[0,4,5,6],[0,7,8,4],[1,3,2,1],[2,8,9,9],[2,9,9,7],[3,6,8,8],[3,7,7,5],[5,6,6,5]]
PD code (use to draw this loop with SnapPy): [[7,20,8,1],[19,6,20,7],[8,18,9,17],[1,4,2,5],[5,18,6,19],[9,14,10,15],[11,16,12,17],[12,3,13,4],[2,13,3,14],[10,16,11,15]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,20,-10,-1)(18,1,-19,-2)(16,3,-17,-4)(19,10,-20,-11)(6,11,-7,-12)(12,7,-13,-8)(8,13,-9,-14)(14,5,-15,-6)(2,15,-3,-16)(4,17,-5,-18)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,18,-5,14,-9)(-2,-16,-4,-18)(-3,16)(-6,-12,-8,-14)(-7,12)(-10,19,1)(-11,6,-15,2,-19)(-13,8)(-17,4)(-20,9,13,7,11)(3,15,5,17)(10,20)
Loop annotated with half-edges
12^1_129 annotated with half-edges