$11^{1}_{30}$ - Minimal pinning sets
Pinning sets for 11^1_30 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_30 Pinning data
Pinning number of this loop: 4
Total number of pinning sets: 128
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: 2.89692
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, 3, 4, 8}
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
7
2.4
6
0
0
21
2.67
7
0
0
35
2.86
8
0
0
35
3.0
9
0
0
21
3.11
10
0
0
7
3.2
11
0
0
1
3.27
Total
1
0
127
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 3, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,4,5],[0,6,6,3],[0,2,7,7],[0,5,1,1],[1,4,7,8],[2,8,8,2],[3,8,5,3],[5,7,6,6]]
PD code (use to draw this loop with SnapPy): [[3,18,4,1],[2,7,3,8],[12,17,13,18],[4,13,5,14],[1,9,2,8],[9,6,10,7],[16,11,17,12],[5,15,6,14],[10,15,11,16]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (6,3,-7,-4)(17,4,-18,-5)(5,16,-6,-17)(13,8,-14,-9)(1,10,-2,-11)(11,2,-12,-3)(7,12,-8,-13)(9,14,-10,-15)(18,15,-1,-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,-11,-3,6,16)(-2,11)(-4,17,-6)(-5,-17)(-7,-13,-9,-15,18,4)(-8,13)(-10,1,15)(-12,7,3)(-14,9)(-16,5,-18)(2,10,14,8,12)
Loop annotated with half-edges
11^1_30 annotated with half-edges