$12^{1}_{11}$ - Minimal pinning sets
Pinning sets for 12^1_11 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_11 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 128
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: 2.90623
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, 7, 9}
5
[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
5
1
0
0
2.0
6
0
0
7
2.38
7
0
0
21
2.65
8
0
0
35
2.86
9
0
0
35
3.02
10
0
0
21
3.14
11
0
0
7
3.25
12
0
0
1
3.33
Total
1
0
127
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 3, 3, 5, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,3,3,4],[0,5,6,0],[0,4,1,1],[1,3,6,7],[2,7,7,8],[2,9,9,4],[4,8,5,5],[5,7,9,9],[6,8,8,6]]
PD code (use to draw this loop with SnapPy): [[3,20,4,1],[9,2,10,3],[19,4,20,5],[1,8,2,9],[10,8,11,7],[5,15,6,14],[18,11,19,12],[6,15,7,16],[16,13,17,14],[12,17,13,18]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (16,1,-17,-2)(4,7,-5,-8)(18,5,-19,-6)(15,8,-16,-9)(13,10,-14,-11)(11,2,-12,-3)(3,12,-4,-13)(9,14,-10,-15)(20,17,-1,-18)(6,19,-7,-20)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,16,8,-5,18)(-2,11,-14,9,-16)(-3,-13,-11)(-4,-8,15,-10,13)(-6,-20,-18)(-7,4,12,2,-17,20)(-9,-15)(-12,3)(-19,6)(1,17)(5,7,19)(10,14)
Loop annotated with half-edges
12^1_11 annotated with half-edges