$11^{1}_{19}$ - Minimal pinning sets
Pinning sets for 11^1_19 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_19 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 96
of which optimal: 2
of which minimal: 2
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.90403
on average over minimal pinning sets: 2.2
on average over optimal pinning sets: 2.2
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 3, 5, 10}
5
[2, 2, 2, 2, 3]
2.20
B (optimal)
• {1, 2, 3, 7, 10}
5
[2, 2, 2, 2, 3]
2.20
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
5
2
0
0
2.2
6
0
0
11
2.55
7
0
0
25
2.79
8
0
0
30
2.97
9
0
0
20
3.1
10
0
0
7
3.2
11
0
0
1
3.27
Total
2
0
94
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,4,4,5],[0,6,3,0],[0,2,6,4],[1,3,7,1],[1,8,8,6],[2,5,7,3],[4,6,8,8],[5,7,7,5]]
PD code (use to draw this loop with SnapPy): [[18,13,1,14],[14,7,15,8],[12,17,13,18],[1,17,2,16],[6,15,7,16],[8,4,9,3],[11,2,12,3],[5,10,6,11],[4,10,5,9]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (10,3,-11,-4)(5,18,-6,-1)(1,6,-2,-7)(14,9,-15,-10)(2,11,-3,-12)(12,15,-13,-16)(8,13,-9,-14)(7,16,-8,-17)(17,4,-18,-5)
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)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,-7,-17,-5)(-2,-12,-16,7)(-3,10,-15,12)(-4,17,-8,-14,-10)(-6,1)(-9,14)(-11,2,6,18,4)(-13,8,16)(-18,5)(3,11)(9,13,15)
Loop annotated with half-edges
11^1_19 annotated with half-edges