$12^{1}_{295}$ - Minimal pinning sets
Pinning sets for 12^1_295 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_295 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, 4, 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, 3, 4, 5, 6, 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],[0,2,7,7],[1,8,9,9],[1,6,6,2],[2,5,5,9],[3,8,8,3],[4,7,7,9],[4,8,6,4]]
PD code (use to draw this loop with SnapPy): [[20,13,1,14],[14,19,15,20],[12,9,13,10],[1,9,2,8],[18,5,19,6],[15,11,16,10],[16,11,17,12],[2,7,3,8],[6,3,7,4],[4,17,5,18]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (4,1,-5,-2)(16,3,-17,-4)(20,5,-1,-6)(6,19,-7,-20)(10,7,-11,-8)(8,13,-9,-14)(14,9,-15,-10)(18,11,-19,-12)(2,15,-3,-16)(12,17,-13,-18)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,4,-17,12,-19,6)(-2,-16,-4)(-3,16)(-5,20,-7,10,-15,2)(-6,-20)(-8,-14,-10)(-9,14)(-11,18,-13,8)(-12,-18)(1,5)(3,15,9,13,17)(7,19,11)
Loop annotated with half-edges
12^1_295 annotated with half-edges