$11^{1}_{91}$ - Minimal pinning sets
Pinning sets for 11^1_91 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_91 Pinning data
Pinning number of this loop: 6
Total number of pinning sets: 32
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: 2.78769
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, 3, 6, 7, 8}
6
[2, 2, 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
6
1
0
0
2.0
7
0
0
5
2.4
8
0
0
10
2.7
9
0
0
10
2.93
10
0
0
5
3.12
11
0
0
1
3.27
Total
1
0
31
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 4, 4, 4, 5, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,2],[0,3,4,0],[0,5,5,0],[1,6,6,7],[1,7,7,5],[2,4,8,2],[3,8,8,3],[3,8,4,4],[5,7,6,6]]
PD code (use to draw this loop with SnapPy): [[9,18,10,1],[17,8,18,9],[10,2,11,1],[5,16,6,17],[7,12,8,13],[2,12,3,11],[15,4,16,5],[6,14,7,13],[3,14,4,15]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (12,1,-13,-2)(14,5,-15,-6)(8,17,-9,-18)(4,9,-5,-10)(10,3,-11,-4)(18,11,-1,-12)(2,13,-3,-14)(6,15,-7,-16)(16,7,-17,-8)
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)(-2,-14,-6,-16,-8,-18,-12)(-3,10,-5,14)(-4,-10)(-7,16)(-9,4,-11,18)(-13,2)(-15,6)(-17,8)(1,11,3,13)(5,9,17,7,15)
Loop annotated with half-edges
11^1_91 annotated with half-edges