$12^{2}_{275}$ - Minimal pinning sets
Pinning sets for 12^2_275 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_275 Pinning data
Pinning number of this multiloop: 6
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: 2.85421
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, 3, 4, 5, 7, 11}
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
6
2.38
8
0
0
15
2.67
9
0
0
20
2.89
10
0
0
15
3.07
11
0
0
6
3.21
12
0
0
1
3.33
Total
1
0
63
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 3, 3, 4, 5, 6, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,5,0],[0,6,6,3],[0,2,7,7],[1,7,8,8],[1,8,9,9],[2,9,9,2],[3,8,4,3],[4,7,5,4],[5,6,6,5]]
PD code (use to draw this multiloop with SnapPy): [[14,20,1,15],[15,13,16,14],[19,7,20,8],[1,7,2,6],[3,12,4,13],[16,11,17,10],[8,18,9,19],[2,5,3,6],[11,4,12,5],[17,9,18,10]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,2,-10,-3)(14,3,-1,-4)(4,13,-5,-14)(16,5,-17,-6)(20,7,-15,-8)(8,19,-9,-20)(1,10,-2,-11)(18,11,-19,-12)(6,15,-7,-16)(12,17,-13,-18)
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,-11,18,-13,4)(-2,9,19,11)(-3,14,-5,16,-7,20,-9)(-4,-14)(-6,-16)(-8,-20)(-10,1,3)(-12,-18)(-15,6,-17,12,-19,8)(2,10)(5,13,17)(7,15)
Multiloop annotated with half-edges
12^2_275 annotated with half-edges