$11^{1}_{26}$ - Minimal pinning sets
Pinning sets for 11^1_26 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_26 Pinning data
Pinning number of this loop: 4
Total number of pinning sets: 160
of which optimal: 1
of which minimal: 2
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.97092
on average over minimal pinning sets: 2.325
on average over optimal pinning sets: 2.25
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 9, 10}
4
[2, 2, 2, 3]
2.25
a (minimal)
• {1, 2, 6, 8, 10}
5
[2, 2, 2, 3, 3]
2.40
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
2.25
5
0
1
7
2.55
6
0
0
26
2.77
7
0
0
45
2.93
8
0
0
45
3.06
9
0
0
26
3.15
10
0
0
8
3.23
11
0
0
1
3.27
Total
1
1
158
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 3, 3, 4, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,3,2,0],[0,1,4,4],[0,5,6,1],[2,7,5,2],[3,4,8,6],[3,5,8,7],[4,6,8,8],[5,7,7,6]]
PD code (use to draw this loop with SnapPy): [[18,9,1,10],[10,17,11,18],[11,8,12,9],[1,16,2,17],[7,12,8,13],[15,6,16,7],[2,6,3,5],[13,5,14,4],[14,3,15,4]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (18,9,-1,-10)(1,16,-2,-17)(11,2,-12,-3)(7,4,-8,-5)(14,5,-15,-6)(3,8,-4,-9)(15,12,-16,-13)(6,13,-7,-14)(10,17,-11,-18)
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)(-2,11,17)(-3,-9,18,-11)(-4,7,13,-16,1,9)(-5,14,-7)(-6,-14)(-8,3,-12,15,5)(-10,-18)(-13,6,-15)(2,16,12)(4,8)
Loop annotated with half-edges
11^1_26 annotated with half-edges