$12^{1}_{14}$ - Minimal pinning sets
Pinning sets for 12^1_14 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_14 Pinning data
Pinning number of this loop: 4
Total number of pinning sets: 256
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: 2.96564
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, 7}
4
[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
4
1
0
0
2.0
5
0
0
8
2.4
6
0
0
28
2.67
7
0
0
56
2.86
8
0
0
70
3.0
9
0
0
56
3.11
10
0
0
28
3.2
11
0
0
8
3.27
12
0
0
1
3.33
Total
1
0
255
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,4,5],[0,5,6,7],[0,7,6,5],[0,5,1,1],[1,4,3,2],[2,3,8,8],[2,9,9,3],[6,9,9,6],[7,8,8,7]]
PD code (use to draw this loop with SnapPy): [[3,20,4,1],[2,11,3,12],[14,19,15,20],[4,9,5,10],[1,13,2,12],[13,10,14,11],[5,18,6,19],[15,8,16,9],[17,6,18,7],[7,16,8,17]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (13,2,-14,-3)(11,4,-12,-5)(20,5,-1,-6)(9,6,-10,-7)(18,7,-19,-8)(8,17,-9,-18)(3,12,-4,-13)(1,14,-2,-15)(10,15,-11,-16)(19,16,-20,-17)
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,-15,10,6)(-2,13,-4,11,15)(-3,-13)(-5,20,16,-11)(-6,9,17,-20)(-7,18,-9)(-8,-18)(-10,-16,19,7)(-12,3,-14,1,5)(-17,8,-19)(2,14)(4,12)
Loop annotated with half-edges
12^1_14 annotated with half-edges