$11^{1}_{43}$ - Minimal pinning sets
Pinning sets for 11^1_43 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_43 Pinning data
Pinning number of this loop: 6
Total number of pinning sets: 32
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: 2.78769
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, 5, 6, 7, 8}
6
[2, 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
6
1
0
0
2.0
7
0
0
5
2.4
8
0
0
10
2.7
9
0
0
10
2.93
10
0
0
5
3.12
11
0
0
1
3.27
Total
1
0
31
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 3, 3, 4, 6, 8]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,2],[0,3,3,0],[0,4,4,0],[1,5,6,1],[2,6,7,2],[3,8,8,6],[3,5,7,4],[4,6,8,8],[5,7,7,5]]
PD code (use to draw this loop with SnapPy): [[18,9,1,10],[10,17,11,18],[8,1,9,2],[16,11,17,12],[2,7,3,8],[12,5,13,6],[6,15,7,16],[3,15,4,14],[4,13,5,14]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,2,-10,-3)(17,4,-18,-5)(15,6,-16,-7)(13,8,-14,-9)(1,10,-2,-11)(11,18,-12,-1)(3,12,-4,-13)(7,14,-8,-15)(5,16,-6,-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,-11)(-2,9,-14,7,-16,5,-18,11)(-3,-13,-9)(-4,17,-6,15,-8,13)(-5,-17)(-7,-15)(-10,1,-12,3)(2,10)(4,12,18)(6,16)(8,14)
Loop annotated with half-edges
11^1_43 annotated with half-edges