$12^{1}_{305}$ - Minimal pinning sets
Pinning sets for 12^1_305 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_305 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, 3, 4, 4, 5, 5, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,4,0],[0,5,6,3],[0,2,7,7],[1,5,5,1],[2,4,4,8],[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): [[20,7,1,8],[8,19,9,20],[11,6,12,7],[1,12,2,13],[18,9,19,10],[10,17,11,18],[5,14,6,15],[2,14,3,13],[3,16,4,17],[15,4,16,5]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,20,-12,-1)(7,2,-8,-3)(16,3,-17,-4)(14,5,-15,-6)(17,8,-18,-9)(9,18,-10,-19)(1,10,-2,-11)(19,12,-20,-13)(6,13,-7,-14)(4,15,-5,-16)
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,-11)(-2,7,13,-20,11)(-3,16,-5,14,-7)(-4,-16)(-6,-14)(-8,17,3)(-9,-19,-13,6,-15,4,-17)(-10,1,-12,19)(-18,9)(2,10,18,8)(5,15)(12,20)
Loop annotated with half-edges
12^1_305 annotated with half-edges