$12^{1}_{47}$ - Minimal pinning sets
Pinning sets for 12^1_47 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_47 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, 9, 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, 3, 4, 4, 4, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,5,6],[0,7,7,8],[0,8,8,6],[0,9,9,1],[1,9,9,6],[1,5,3,7],[2,6,8,2],[2,7,3,3],[4,5,5,4]]
PD code (use to draw this loop with SnapPy): [[5,20,6,1],[4,13,5,14],[19,8,20,9],[6,11,7,12],[1,15,2,14],[16,3,17,4],[17,12,18,13],[9,18,10,19],[10,7,11,8],[15,3,16,2]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (13,20,-14,-1)(7,4,-8,-5)(16,5,-17,-6)(3,8,-4,-9)(14,9,-15,-10)(1,10,-2,-11)(11,18,-12,-19)(6,15,-7,-16)(2,17,-3,-18)(19,12,-20,-13)
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,-13)(-2,-18,11)(-3,-9,14,20,12,18)(-4,7,15,9)(-5,16,-7)(-6,-16)(-8,3,17,5)(-10,1,-14)(-12,19)(-15,6,-17,2,10)(-20,13)(4,8)
Loop annotated with half-edges
12^1_47 annotated with half-edges