$12^{1}_{12}$ - Minimal pinning sets
Pinning sets for 12^1_12 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_12 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, 5, 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, 3, 3, 4, 4, 7, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,4,5],[0,6,7,7],[0,7,7,6],[0,5,1,1],[1,4,8,8],[2,9,9,3],[2,3,3,2],[5,9,9,5],[6,8,8,6]]
PD code (use to draw this loop with SnapPy): [[3,20,4,1],[2,11,3,12],[19,6,20,7],[4,18,5,17],[1,13,2,12],[13,10,14,11],[7,16,8,17],[5,18,6,19],[9,14,10,15],[15,8,16,9]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (17,4,-18,-5)(13,6,-14,-7)(11,8,-12,-9)(20,9,-1,-10)(10,19,-11,-20)(7,12,-8,-13)(5,14,-6,-15)(15,2,-16,-3)(3,16,-4,-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,-19,10)(-2,15,-6,13,-8,11,19)(-3,-17,-5,-15)(-4,17)(-7,-13)(-9,20,-11)(-10,-20)(-12,7,-14,5,-18,1,9)(-16,3)(2,18,4,16)(6,14)(8,12)
Loop annotated with half-edges
12^1_12 annotated with half-edges