$12^{1}_{151}$ - Minimal pinning sets
Pinning sets for 12^1_151 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_151 Pinning data
Pinning number of this loop: 7
Total number of pinning sets: 32
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: 2.80821
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, 6, 7, 8, 9}
7
[2, 2, 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
7
1
0
0
2.0
8
0
0
5
2.4
9
0
0
10
2.71
10
0
0
10
2.96
11
0
0
5
3.16
12
0
0
1
3.33
Total
1
0
31
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 6, 9]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,2],[0,3,3,0],[0,4,4,0],[1,5,6,1],[2,6,7,2],[3,8,8,6],[3,5,7,4],[4,6,9,9],[5,9,9,5],[7,8,8,7]]
PD code (use to draw this loop with SnapPy): [[9,20,10,1],[19,8,20,9],[10,2,11,1],[7,18,8,19],[2,12,3,11],[6,13,7,14],[17,12,18,13],[3,17,4,16],[14,5,15,6],[4,15,5,16]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,2,-12,-3)(16,5,-17,-6)(8,19,-9,-20)(14,9,-15,-10)(3,10,-4,-11)(1,12,-2,-13)(13,20,-14,-1)(4,15,-5,-16)(6,17,-7,-18)(18,7,-19,-8)
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)(-2,11,-4,-16,-6,-18,-8,-20,13)(-3,-11)(-5,16)(-7,18)(-9,14,20)(-10,3,-12,1,-14)(-15,4,10)(-17,6)(-19,8)(2,12)(5,15,9,19,7,17)
Loop annotated with half-edges
12^1_151 annotated with half-edges