$12^{1}_{248}$ - Minimal pinning sets
Pinning sets for 12^1_248 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_248 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)
• {2, 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, 4, 4, 4, 4, 4, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,6,6],[0,6,3,3],[0,2,2,7],[0,8,8,5],[1,4,9,7],[1,7,2,1],[3,6,5,9],[4,9,9,4],[5,8,8,7]]
PD code (use to draw this loop with SnapPy): [[17,20,18,1],[5,16,6,17],[19,14,20,15],[18,14,19,13],[1,10,2,11],[11,4,12,5],[15,6,16,7],[7,12,8,13],[9,2,10,3],[3,8,4,9]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (8,1,-9,-2)(12,3,-13,-4)(20,5,-1,-6)(18,7,-19,-8)(4,9,-5,-10)(10,15,-11,-16)(16,11,-17,-12)(2,13,-3,-14)(14,17,-15,-18)(6,19,-7,-20)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,8,-19,6)(-2,-14,-18,-8)(-3,12,-17,14)(-4,-10,-16,-12)(-5,20,-7,18,-15,10)(-6,-20)(-9,4,-13,2)(-11,16)(1,5,9)(3,13)(7,19)(11,15,17)
Loop annotated with half-edges
12^1_248 annotated with half-edges