$12^{1}_{33}$ - Minimal pinning sets
Pinning sets for 12^1_33 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_33 Pinning data
Pinning number of this loop: 6
Total number of pinning sets: 64
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: 2.85421
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, 3, 4, 7, 11}
6
[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
6
1
0
0
2.0
7
0
0
6
2.38
8
0
0
15
2.67
9
0
0
20
2.89
10
0
0
15
3.07
11
0
0
6
3.21
12
0
0
1
3.33
Total
1
0
63
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 4, 4, 5, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,4,0],[0,5,5,6],[0,7,7,4],[1,3,5,1],[2,4,8,2],[2,9,9,7],[3,6,8,3],[5,7,9,9],[6,8,8,6]]
PD code (use to draw this loop with SnapPy): [[15,20,16,1],[19,14,20,15],[16,7,17,8],[1,12,2,13],[13,18,14,19],[6,17,7,18],[8,4,9,3],[11,2,12,3],[5,10,6,11],[4,10,5,9]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (12,3,-13,-4)(5,20,-6,-1)(1,6,-2,-7)(17,8,-18,-9)(15,10,-16,-11)(2,13,-3,-14)(9,14,-10,-15)(11,16,-12,-17)(7,18,-8,-19)(19,4,-20,-5)
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,-7,-19,-5)(-2,-14,9,-18,7)(-3,12,16,10,14)(-4,19,-8,17,-12)(-6,1)(-9,-15,-11,-17)(-10,15)(-13,2,6,20,4)(-16,11)(-20,5)(3,13)(8,18)
Loop annotated with half-edges
12^1_33 annotated with half-edges