$12^{1}_{75}$ - Minimal pinning sets
Pinning sets for 12^1_75 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_75 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)
• {1, 3, 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, 4, 4, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,5,6],[0,7,7,3],[0,2,8,9],[0,6,5,5],[1,4,4,1],[1,4,9,7],[2,6,8,2],[3,7,9,9],[3,8,8,6]]
PD code (use to draw this loop with SnapPy): [[20,13,1,14],[14,3,15,4],[8,19,9,20],[9,12,10,13],[1,17,2,16],[2,15,3,16],[4,17,5,18],[18,7,19,8],[11,6,12,7],[10,6,11,5]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (12,1,-13,-2)(3,8,-4,-9)(9,4,-10,-5)(16,5,-17,-6)(7,10,-8,-11)(18,11,-19,-12)(20,13,-1,-14)(14,19,-15,-20)(2,15,-3,-16)(6,17,-7,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,12,-19,14)(-2,-16,-6,-18,-12)(-3,-9,-5,16)(-4,9)(-7,-11,18)(-8,3,15,19,11)(-10,7,17,5)(-13,20,-15,2)(-14,-20)(-17,6)(1,13)(4,8,10)
Loop annotated with half-edges
12^1_75 annotated with half-edges