$10^{1}_{13}$ - Minimal pinning sets
Pinning sets for 10^1_13 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^1_13 Pinning data
Pinning number of this loop: 4
Total number of pinning sets: 96
of which optimal: 2
of which minimal: 2
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.89501
on average over minimal pinning sets: 2.25
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, 4, 9}
4
[2, 2, 2, 3]
2.25
B (optimal)
• {1, 2, 3, 9}
4
[2, 2, 2, 3]
2.25
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
4
2
0
0
2.25
5
0
0
11
2.58
6
0
0
25
2.8
7
0
0
30
2.95
8
0
0
20
3.06
9
0
0
7
3.14
10
0
0
1
3.2
Total
2
0
94
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 4, 4, 4, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,5,2],[0,1,5,6],[0,7,7,4],[0,3,6,5],[1,4,2,1],[2,4,7,7],[3,6,6,3]]
PD code (use to draw this loop with SnapPy): [[16,5,1,6],[6,14,7,13],[15,12,16,13],[4,9,5,10],[1,9,2,8],[14,8,15,7],[2,11,3,12],[10,3,11,4]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (7,16,-8,-1)(13,2,-14,-3)(4,11,-5,-12)(5,14,-6,-15)(1,6,-2,-7)(15,8,-16,-9)(12,9,-13,-10)(10,3,-11,-4)
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)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,-7)(-2,13,9,-16,7)(-3,10,-13)(-4,-12,-10)(-5,-15,-9,12)(-6,1,-8,15)(-11,4)(-14,5,11,3)(2,6,14)(8,16)
Loop annotated with half-edges
10^1_13 annotated with half-edges