$12^{1}_{358}$ - Minimal pinning sets
Pinning sets for 12^1_358 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_358 Pinning data
Pinning number of this loop: 4
Total number of pinning sets: 256
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: 2.96564
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, 5, 11}
4
[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
4
1
0
0
2.0
5
0
0
8
2.4
6
0
0
28
2.67
7
0
0
56
2.86
8
0
0
70
3.0
9
0
0
56
3.11
10
0
0
28
3.2
11
0
0
8
3.27
12
0
0
1
3.33
Total
1
0
255
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,3,4,5],[0,6,6,0],[0,7,8,1],[1,8,8,5],[1,4,9,6],[2,5,7,2],[3,6,9,9],[3,9,4,4],[5,8,7,7]]
PD code (use to draw this loop with SnapPy): [[5,20,6,1],[4,11,5,12],[19,6,20,7],[1,13,2,12],[16,3,17,4],[17,10,18,11],[7,18,8,19],[13,8,14,9],[2,15,3,16],[9,14,10,15]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (13,20,-14,-1)(16,3,-17,-4)(10,5,-11,-6)(14,7,-15,-8)(1,8,-2,-9)(9,18,-10,-19)(6,11,-7,-12)(19,12,-20,-13)(4,15,-5,-16)(2,17,-3,-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,-9,-19,-13)(-2,-18,9)(-3,16,-5,10,18)(-4,-16)(-6,-12,19,-10)(-7,14,20,12)(-8,1,-14)(-11,6)(-15,4,-17,2,8)(-20,13)(3,17)(5,15,7,11)
Loop annotated with half-edges
12^1_358 annotated with half-edges