$12^{1}_{98}$ - Minimal pinning sets
Pinning sets for 12^1_98 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_98 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, 3, 3, 4, 4, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,4,5],[0,6,6,3],[0,2,7,8],[0,5,1,1],[1,4,9,9],[2,9,7,2],[3,6,8,8],[3,7,7,9],[5,8,6,5]]
PD code (use to draw this loop with SnapPy): [[3,20,4,1],[15,2,16,3],[19,8,20,9],[4,8,5,7],[1,14,2,15],[16,14,17,13],[9,18,10,19],[5,10,6,11],[11,6,12,7],[17,12,18,13]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (13,20,-14,-1)(9,4,-10,-5)(5,2,-6,-3)(17,6,-18,-7)(3,8,-4,-9)(15,10,-16,-11)(11,14,-12,-15)(19,12,-20,-13)(7,16,-8,-17)(1,18,-2,-19)
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,-19,-13)(-2,5,-10,15,-12,19)(-3,-9,-5)(-4,9)(-6,17,-8,3)(-7,-17)(-11,-15)(-14,11,-16,7,-18,1)(-20,13)(2,18,6)(4,8,16,10)(12,14,20)
Loop annotated with half-edges
12^1_98 annotated with half-edges