$12^{1}_{311}$ - Minimal pinning sets
Pinning sets for 12^1_311 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_311 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, 3, 4, 5, 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, 3, 3, 4, 5, 6, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,4,5],[0,6,6,7],[0,7,8,0],[1,8,5,1],[1,4,9,9],[2,9,9,2],[2,8,8,3],[3,7,7,4],[5,6,6,5]]
PD code (use to draw this loop with SnapPy): [[20,5,1,6],[6,15,7,16],[19,10,20,11],[4,1,5,2],[14,7,15,8],[16,14,17,13],[11,18,12,19],[9,2,10,3],[3,8,4,9],[17,12,18,13]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (17,2,-18,-3)(11,4,-12,-5)(20,5,-1,-6)(16,7,-17,-8)(14,9,-15,-10)(10,13,-11,-14)(3,12,-4,-13)(8,15,-9,-16)(1,18,-2,-19)(6,19,-7,-20)
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,-19,6)(-2,17,7,19)(-3,-13,10,-15,8,-17)(-4,11,13)(-5,20,-7,16,-9,14,-11)(-6,-20)(-8,-16)(-10,-14)(-12,3,-18,1,5)(2,18)(4,12)(9,15)
Loop annotated with half-edges
12^1_311 annotated with half-edges