$12^{1}_{51}$ - Minimal pinning sets
Pinning sets for 12^1_51 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_51 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, 2, 3, 4, 11}
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, 3, 5, 5, 8]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,4,5],[0,6,7,3],[0,2,8,8],[0,5,1,1],[1,4,6,6],[2,5,5,7],[2,6,9,9],[3,9,9,3],[7,8,8,7]]
PD code (use to draw this loop with SnapPy): [[3,20,4,1],[11,2,12,3],[14,19,15,20],[4,15,5,16],[1,10,2,11],[12,10,13,9],[13,8,14,9],[18,7,19,8],[5,17,6,16],[6,17,7,18]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,20,-10,-1)(16,5,-17,-6)(11,6,-12,-7)(7,10,-8,-11)(19,8,-20,-9)(2,13,-3,-14)(14,3,-15,-4)(4,15,-5,-16)(12,17,-13,-18)(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,-9)(-2,-14,-4,-16,-6,11,-8,19)(-3,14)(-5,16)(-7,-11)(-10,7,-12,-18,1)(-13,2,18)(-15,4)(-17,12,6)(-20,9)(3,13,17,5,15)(8,10,20)
Loop annotated with half-edges
12^1_51 annotated with half-edges