$12^{1}_{254}$ - Minimal pinning sets
Pinning sets for 12^1_254
Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_254
Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 288
of which optimal: 4
of which minimal: 4
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 3.03466
on average over minimal pinning sets: 2.4
on average over optimal pinning sets: 2.4
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
•
{1, 3, 5, 7, 11}
5
[2, 2, 2, 3, 3]
2.40
B (optimal)
•
{1, 2, 5, 7, 11}
5
[2, 2, 2, 3, 3]
2.40
C (optimal)
•
{1, 3, 5, 8, 11}
5
[2, 2, 2, 3, 3]
2.40
D (optimal)
•
{1, 2, 5, 8, 11}
5
[2, 2, 2, 3, 3]
2.40
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
5
4
0
0
2.4
6
0
0
24
2.69
7
0
0
61
2.9
8
0
0
85
3.05
9
0
0
70
3.16
10
0
0
34
3.24
11
0
0
9
3.29
12
0
0
1
3.33
Total
4
0
284
Other information about this loop
Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,6,2],[0,1,3,3],[0,2,2,7],[0,8,5,5],[1,4,4,6],[1,5,8,9],[3,9,9,8],[4,7,9,6],[6,8,7,7]]
PD code (use to draw this loop with SnapPy): [[17,20,18,1],[3,16,4,17],[4,19,5,20],[18,5,19,6],[1,11,2,10],[2,9,3,10],[15,8,16,9],[6,13,7,14],[11,14,12,15],[12,7,13,8]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (16,3,-17,-4)(10,5,-11,-6)(13,6,-14,-7)(20,7,-1,-8)(8,19,-9,-20)(4,11,-5,-12)(9,12,-10,-13)(1,14,-2,-15)(2,17,-3,-18)(15,18,-16,-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,-15,-19,8)(-2,-18,15)(-3,16,18)(-4,-12,9,19,-16)(-5,10,12)(-6,13,-10)(-7,20,-9,-13)(-8,-20)(-11,4,-17,2,14,6)(-14,1,7)(3,17)(5,11)
Loop annotated with half-edges
12^1_254 annotated with half-edges