$12^{1}_{253}$ - Minimal pinning sets
Pinning sets for 12^1_253 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_253 Pinning data
Pinning number of this loop: 4
Total number of pinning sets: 256
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: 2.96564
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)
• {2, 4, 5, 11}
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
8
2.4
6
0
0
28
2.67
7
0
0
56
2.86
8
0
0
70
3.0
9
0
0
56
3.11
10
0
0
28
3.2
11
0
0
8
3.27
12
0
0
1
3.33
Total
1
0
255
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,6,2],[0,1,7,7],[0,7,7,8],[0,9,5,5],[1,4,4,6],[1,5,9,8],[2,3,3,2],[3,6,9,9],[4,8,8,6]]
PD code (use to draw this loop with SnapPy): [[20,7,1,8],[8,3,9,4],[4,19,5,20],[6,17,7,18],[1,15,2,14],[2,13,3,14],[9,13,10,12],[18,5,19,6],[16,11,17,12],[15,11,16,10]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (6,1,-7,-2)(16,3,-17,-4)(18,5,-19,-6)(8,13,-9,-14)(14,9,-15,-10)(10,7,-11,-8)(20,11,-1,-12)(12,19,-13,-20)(4,15,-5,-16)(2,17,-3,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,6,-19,12)(-2,-18,-6)(-3,16,-5,18)(-4,-16)(-7,10,-15,4,-17,2)(-8,-14,-10)(-9,14)(-11,20,-13,8)(-12,-20)(1,11,7)(3,17)(5,15,9,13,19)
Loop annotated with half-edges
12^1_253 annotated with half-edges