$11^{1}_{53}$ - Minimal pinning sets
Pinning sets for 11^1_53 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_53 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 136
of which optimal: 3
of which minimal: 4
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.9775
on average over minimal pinning sets: 2.46667
on average over optimal pinning sets: 2.4
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {3, 4, 6, 10, 11}
5
[2, 2, 2, 3, 3]
2.40
B (optimal)
• {1, 3, 5, 6, 10}
5
[2, 2, 2, 3, 3]
2.40
C (optimal)
• {1, 3, 4, 6, 10}
5
[2, 2, 2, 3, 3]
2.40
a (minimal)
• {2, 3, 5, 6, 10, 11}
6
[2, 2, 2, 3, 3, 4]
2.67
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
5
3
0
0
2.4
6
0
1
16
2.69
7
0
0
38
2.89
8
0
0
43
3.05
9
0
0
26
3.15
10
0
0
8
3.23
11
0
0
1
3.27
Total
3
1
132
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,4,5,6],[0,6,7,0],[0,5,4,4],[1,3,3,5],[1,4,3,8],[1,8,7,2],[2,6,8,8],[5,7,7,6]]
PD code (use to draw this loop with SnapPy): [[18,9,1,10],[10,3,11,4],[8,17,9,18],[1,12,2,13],[13,2,14,3],[11,14,12,15],[4,7,5,8],[5,16,6,17],[15,6,16,7]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,18,-12,-1)(8,1,-9,-2)(13,4,-14,-5)(2,5,-3,-6)(16,7,-17,-8)(17,10,-18,-11)(9,12,-10,-13)(3,14,-4,-15)(6,15,-7,-16)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,8,-17,-11)(-2,-6,-16,-8)(-3,-15,6)(-4,13,-10,17,7,15)(-5,2,-9,-13)(-7,16)(-12,9,1)(-14,3,5)(-18,11)(4,14)(10,12,18)
Loop annotated with half-edges
11^1_53 annotated with half-edges