$12^{1}_{310}$ - Minimal pinning sets
Pinning sets for 12^1_310
Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_310
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, 6, 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, 5, 5, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,2,0],[0,1,5,5],[0,6,7,7],[1,8,9,9],[2,6,6,2],[3,5,5,9],[3,8,8,3],[4,7,7,9],[4,8,6,4]]
PD code (use to draw this loop with SnapPy): [[13,20,14,1],[19,12,20,13],[14,12,15,11],[1,9,2,8],[18,5,19,6],[15,10,16,11],[9,16,10,17],[2,7,3,8],[6,3,7,4],[4,17,5,18]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (13,20,-14,-1)(17,2,-18,-3)(3,16,-4,-17)(10,5,-11,-6)(6,9,-7,-10)(14,7,-15,-8)(4,11,-5,-12)(19,12,-20,-13)(8,15,-9,-16)(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)(-2,17,-4,-12,19)(-3,-17)(-5,10,-7,14,20,12)(-6,-10)(-8,-16,3,-18,1,-14)(-9,6,-11,4,16)(-15,8)(-20,13)(2,18)(5,11)(7,9,15)
Loop annotated with half-edges
12^1_310 annotated with half-edges