$11^{1}_{11}$ - Minimal pinning sets
Pinning sets for 11^1_11 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_11 Pinning data
Pinning number of this loop: 3
Total number of pinning sets: 256
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: 2.96519
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, 10}
3
[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
3
1
0
0
2.0
4
0
0
8
2.44
5
0
0
28
2.7
6
0
0
56
2.87
7
0
0
70
3.0
8
0
0
56
3.09
9
0
0
28
3.17
10
0
0
8
3.22
11
0
0
1
3.27
Total
1
0
255
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,4,5],[0,5,6,7],[0,7,6,5],[0,5,1,1],[1,4,3,2],[2,3,8,8],[2,8,8,3],[6,7,7,6]]
PD code (use to draw this loop with SnapPy): [[3,18,4,1],[11,2,12,3],[17,8,18,9],[4,14,5,13],[1,10,2,11],[12,10,13,9],[5,16,6,17],[7,14,8,15],[15,6,16,7]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,18,-10,-1)(13,4,-14,-5)(15,6,-16,-7)(7,10,-8,-11)(17,8,-18,-9)(11,2,-12,-3)(5,12,-6,-13)(3,14,-4,-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)(-2,11,-8,17)(-3,-15,-7,-11)(-4,13,-6,15)(-5,-13)(-10,7,-16,1)(-12,5,-14,3)(-18,9)(2,16,6,12)(4,14)(8,10,18)
Loop annotated with half-edges
11^1_11 annotated with half-edges