$12^{1}_{134}$ - Minimal pinning sets
Pinning sets for 12^1_134 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_134 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, 4, 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, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,5,5],[0,6,6,7],[0,4,4,0],[1,3,3,7],[1,8,9,1],[2,9,7,2],[2,6,8,4],[5,7,9,9],[5,8,8,6]]
PD code (use to draw this loop with SnapPy): [[9,20,10,1],[3,8,4,9],[14,19,15,20],[10,2,11,1],[11,2,12,3],[7,4,8,5],[18,13,19,14],[15,13,16,12],[5,16,6,17],[17,6,18,7]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (3,20,-4,-1)(13,2,-14,-3)(19,4,-20,-5)(8,11,-9,-12)(14,9,-15,-10)(1,12,-2,-13)(10,15,-11,-16)(5,16,-6,-17)(17,6,-18,-7)(7,18,-8,-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,-13,-3)(-2,13)(-4,19,-8,-12,1)(-5,-17,-7,-19)(-6,17)(-9,14,2,12)(-10,-16,5,-20,3,-14)(-11,8,18,6,16)(-15,10)(-18,7)(4,20)(9,11,15)
Loop annotated with half-edges
12^1_134 annotated with half-edges