$11^{1}_{15}$ - Minimal pinning sets
Pinning sets for 11^1_15 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_15 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, 8, 10}
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, 4, 4, 4, 4, 4, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,4,4,2],[0,1,5,0],[0,6,7,4],[1,3,5,1],[2,4,7,6],[3,5,8,8],[3,8,8,5],[6,7,7,6]]
PD code (use to draw this loop with SnapPy): [[18,9,1,10],[10,7,11,8],[8,17,9,18],[1,13,2,12],[6,11,7,12],[16,5,17,6],[13,5,14,4],[2,15,3,16],[14,3,15,4]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (18,9,-1,-10)(12,1,-13,-2)(6,3,-7,-4)(14,5,-15,-6)(2,7,-3,-8)(8,15,-9,-16)(16,11,-17,-12)(4,13,-5,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,12,-17,10)(-2,-8,-16,-12)(-3,6,-15,8)(-4,-14,-6)(-5,14)(-7,2,-13,4)(-9,18,-11,16)(-10,-18)(1,9,15,5,13)(3,7)(11,17)
Loop annotated with half-edges
11^1_15 annotated with half-edges