$12^{1}_{252}$ - Minimal pinning sets
Pinning sets for 12^1_252 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_252 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, 3, 4, 9}
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, 3, 4, 4, 4, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,5,0],[0,5,6,3],[0,2,7,4],[1,3,8,8],[1,6,6,2],[2,5,5,9],[3,9,9,8],[4,7,9,4],[6,8,7,7]]
PD code (use to draw this loop with SnapPy): [[7,20,8,1],[19,6,20,7],[8,11,9,12],[1,12,2,13],[13,18,14,19],[10,5,11,6],[9,5,10,4],[2,16,3,15],[17,14,18,15],[3,16,4,17]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (20,5,-1,-6)(6,1,-7,-2)(15,2,-16,-3)(4,7,-5,-8)(17,8,-18,-9)(13,10,-14,-11)(11,18,-12,-19)(19,12,-20,-13)(9,14,-10,-15)(3,16,-4,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,6)(-2,15,-10,13,-20,-6)(-3,-17,-9,-15)(-4,-8,17)(-5,20,12,18,8)(-7,4,16,2)(-11,-19,-13)(-12,19)(-14,9,-18,11)(-16,3)(1,5,7)(10,14)
Loop annotated with half-edges
12^1_252 annotated with half-edges