$12^{2}_{79}$ - Minimal pinning sets
Pinning sets for 12^2_79 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_79 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 160
of which optimal: 1
of which minimal: 2
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.97043
on average over minimal pinning sets: 2.26667
on average over optimal pinning sets: 2.2
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 5, 7, 11}
5
[2, 2, 2, 2, 3]
2.20
a (minimal)
• {1, 3, 4, 5, 7, 11}
6
[2, 2, 2, 2, 3, 3]
2.33
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
2.2
6
0
1
7
2.5
7
0
0
26
2.74
8
0
0
45
2.92
9
0
0
45
3.07
10
0
0
26
3.18
11
0
0
8
3.27
12
0
0
1
3.33
Total
1
1
158
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 3, 4, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,3,4,0],[0,4,4,5],[0,6,6,1],[1,7,2,2],[2,8,9,6],[3,5,9,3],[4,9,8,8],[5,7,7,9],[5,8,7,6]]
PD code (use to draw this multiloop with SnapPy): [[16,20,1,17],[17,15,18,16],[7,19,8,20],[1,14,2,15],[18,6,19,7],[8,4,9,3],[13,2,14,3],[10,5,11,6],[4,11,5,12],[9,12,10,13]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,16,-12,-1)(1,6,-2,-7)(8,3,-9,-4)(17,4,-18,-5)(2,9,-3,-10)(7,10,-8,-11)(15,12,-16,-13)(20,13,-17,-14)(5,18,-6,-19)(14,19,-15,-20)
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,-7,-11)(-2,-10,7)(-3,8,10)(-4,17,13,-16,11,-8)(-5,-19,14,-17)(-6,1,-12,15,19)(-9,2,6,18,4)(-13,20,-15)(-14,-20)(-18,5)(3,9)(12,16)
Multiloop annotated with half-edges
12^2_79 annotated with half-edges