$11^{1}_{12}$ - Minimal pinning sets
Pinning sets for 11^1_12 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_12 Pinning data
Pinning number of this loop: 3
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: 2.96519
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, 2, 10}
3
[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
3
1
0
0
2.0
4
0
0
8
2.44
5
0
0
28
2.7
6
0
0
56
2.88
7
0
0
70
3.0
8
0
0
56
3.09
9
0
0
28
3.17
10
0
0
8
3.23
11
0
0
1
3.27
Total
1
0
255
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,4,5],[0,5,6,7],[0,8,8,5],[0,5,1,1],[1,4,3,2],[2,8,7,7],[2,6,6,8],[3,7,6,3]]
PD code (use to draw this loop with SnapPy): [[3,18,4,1],[2,11,3,12],[14,17,15,18],[4,9,5,10],[1,13,2,12],[13,10,14,11],[16,7,17,8],[15,7,16,6],[8,5,9,6]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (6,3,-7,-4)(4,13,-5,-14)(14,5,-15,-6)(2,7,-3,-8)(11,8,-12,-9)(18,9,-1,-10)(10,17,-11,-18)(12,15,-13,-16)(1,16,-2,-17)
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,-17,10)(-2,-8,11,17)(-3,6,-15,12,8)(-4,-14,-6)(-5,14)(-7,2,16,-13,4)(-9,18,-11)(-10,-18)(-12,-16,1,9)(3,7)(5,13,15)
Loop annotated with half-edges
11^1_12 annotated with half-edges