$12^{2}_{274}$ - Minimal pinning sets
Pinning sets for 12^2_274 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_274 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, 2, 4, 5, 8, 9}
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, 6, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,4,0],[0,5,5,3],[0,2,6,6],[1,7,8,1],[2,8,8,2],[3,9,7,3],[4,6,9,9],[4,9,5,5],[6,8,7,7]]
PD code (use to draw this multiloop with SnapPy): [[12,20,1,13],[13,11,14,12],[19,7,20,8],[1,7,2,6],[10,14,11,15],[8,18,9,19],[2,5,3,6],[15,3,16,4],[17,9,18,10],[4,16,5,17]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (20,1,-13,-2)(12,3,-1,-4)(4,11,-5,-12)(16,5,-17,-6)(14,7,-15,-8)(18,9,-19,-10)(2,13,-3,-14)(6,15,-7,-16)(10,17,-11,-18)(8,19,-9,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,20,-9,18,-11,4)(-2,-14,-8,-20)(-3,12,-5,16,-7,14)(-4,-12)(-6,-16)(-10,-18)(-13,2)(-15,6,-17,10,-19,8)(1,3,13)(5,11,17)(7,15)(9,19)
Multiloop annotated with half-edges
12^2_274 annotated with half-edges