$12^{1}_{245}$ - Minimal pinning sets
Pinning sets for 12^1_245 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_245 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, 6, 7, 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, 4, 4, 4, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,4,5,5],[0,6,6,0],[0,7,4,4],[1,3,3,7],[1,7,8,1],[2,8,9,2],[3,9,5,4],[5,9,9,6],[6,8,8,7]]
PD code (use to draw this loop with SnapPy): [[13,20,14,1],[3,12,4,13],[19,14,20,15],[1,6,2,7],[7,2,8,3],[11,4,12,5],[15,18,16,19],[5,8,6,9],[17,10,18,11],[16,10,17,9]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (5,20,-6,-1)(9,2,-10,-3)(19,4,-20,-5)(3,6,-4,-7)(7,14,-8,-15)(15,8,-16,-9)(1,10,-2,-11)(17,12,-18,-13)(13,16,-14,-17)(11,18,-12,-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,-11,-19,-5)(-2,9,-16,13,-18,11)(-3,-7,-15,-9)(-4,19,-12,17,-14,7)(-6,3,-10,1)(-8,15)(-13,-17)(-20,5)(2,10)(4,6,20)(8,14,16)(12,18)
Loop annotated with half-edges
12^1_245 annotated with half-edges