$11^{1}_{93}$ - Minimal pinning sets
Pinning sets for 11^1_93 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_93 Pinning data
Pinning number of this loop: 4
Total number of pinning sets: 256
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: 3.05597
on average over minimal pinning sets: 2.5875
on average over optimal pinning sets: 2.58333
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {3, 4, 6, 11}
4
[2, 2, 3, 3]
2.50
B (optimal)
• {2, 3, 6, 11}
4
[2, 2, 3, 4]
2.75
C (optimal)
• {1, 3, 6, 11}
4
[2, 2, 3, 3]
2.50
a (minimal)
• {1, 3, 6, 8, 10}
5
[2, 2, 3, 3, 3]
2.60
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
4
3
0
0
2.58
5
0
1
18
2.8
6
0
0
51
2.95
7
0
0
75
3.06
8
0
0
65
3.14
9
0
0
33
3.2
10
0
0
9
3.24
11
0
0
1
3.27
Total
3
1
252
Other information about this loop Properties
Region degree sequence: [2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,3,4,5],[0,5,6,0],[0,7,4,1],[1,3,7,5],[1,4,8,2],[2,8,8,7],[3,6,8,4],[5,7,6,6]]
PD code (use to draw this loop with SnapPy): [[18,5,1,6],[6,13,7,14],[4,17,5,18],[1,12,2,13],[7,2,8,3],[14,3,15,4],[16,9,17,10],[11,8,12,9],[15,11,16,10]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (5,18,-6,-1)(12,1,-13,-2)(16,3,-17,-4)(9,6,-10,-7)(14,7,-15,-8)(8,13,-9,-14)(17,10,-18,-11)(4,11,-5,-12)(2,15,-3,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,12,-5)(-2,-16,-4,-12)(-3,16)(-6,9,13,1)(-7,14,-9)(-8,-14)(-10,17,3,15,7)(-11,4,-17)(-13,8,-15,2)(-18,5,11)(6,18,10)
Loop annotated with half-edges
11^1_93 annotated with half-edges