$11^{1}_{10}$ - Minimal pinning sets
Pinning sets for 11^1_10 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_10 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 64
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: 2.83846
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, 10}
5
[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
5
1
0
0
2.0
6
0
0
6
2.39
7
0
0
15
2.67
8
0
0
20
2.88
9
0
0
15
3.04
10
0
0
6
3.17
11
0
0
1
3.27
Total
1
0
63
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 3, 4, 4, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,3,3,4],[0,5,6,0],[0,4,1,1],[1,3,7,7],[2,7,8,8],[2,8,8,7],[4,6,5,4],[5,6,6,5]]
PD code (use to draw this loop with SnapPy): [[3,18,4,1],[11,2,12,3],[17,4,18,5],[1,10,2,11],[12,10,13,9],[5,14,6,15],[7,16,8,17],[13,8,14,9],[6,16,7,15]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,18,-10,-1)(15,2,-16,-3)(11,6,-12,-7)(7,10,-8,-11)(17,8,-18,-9)(3,12,-4,-13)(13,4,-14,-5)(5,14,-6,-15)(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,-9)(-2,15,-6,11,-8,17)(-3,-13,-5,-15)(-4,13)(-7,-11)(-10,7,-12,3,-16,1)(-14,5)(-18,9)(2,16)(4,12,6,14)(8,10,18)
Loop annotated with half-edges
11^1_10 annotated with half-edges