$12^{2}_{92}$ - Minimal pinning sets
Pinning sets for 12^2_92 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_92 Pinning data
Pinning number of this multiloop: 3
Total number of pinning sets: 512
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: 3.03436
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)
• {3, 5, 9}
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
9
2.44
5
0
0
36
2.71
6
0
0
84
2.89
7
0
0
126
3.02
8
0
0
126
3.11
9
0
0
84
3.19
10
0
0
36
3.24
11
0
0
9
3.29
12
0
0
1
3.33
Total
1
0
511
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,4,5],[0,5,6,7],[0,7,7,8],[0,5,1,1],[1,4,9,2],[2,9,9,8],[2,8,3,3],[3,7,6,9],[5,8,6,6]]
PD code (use to draw this multiloop with SnapPy): [[3,14,4,1],[9,2,10,3],[13,6,14,7],[4,15,5,20],[1,8,2,9],[10,8,11,7],[18,12,19,13],[5,15,6,16],[16,19,17,20],[11,17,12,18]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (7,14,-8,-1)(11,4,-12,-5)(5,8,-6,-9)(13,6,-14,-7)(19,10,-20,-11)(1,12,-2,-13)(9,18,-10,-19)(17,20,-18,-15)(15,2,-16,-3)(3,16,-4,-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)(-19,19)(-20,20)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,-13,-7)(-2,15,-18,9,-6,13)(-3,-17,-15)(-4,11,-20,17)(-5,-9,-19,-11)(-8,5,-12,1)(-10,19)(-14,7)(-16,3)(2,12,4,16)(6,8,14)(10,18,20)
Multiloop annotated with half-edges
12^2_92 annotated with half-edges