$12^{3}_{29}$ - Minimal pinning sets
Pinning sets for 12^3_29
Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^3_29
Pinning data
Pinning number of this multiloop: 4
Total number of pinning sets: 256
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: 2.96564
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, 4, 7, 11}
4
[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
4
1
0
0
2.0
5
0
0
8
2.4
6
0
0
28
2.67
7
0
0
56
2.86
8
0
0
70
3.0
9
0
0
56
3.11
10
0
0
28
3.2
11
0
0
8
3.27
12
0
0
1
3.33
Total
1
0
255
Other information about this multiloop
Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,2,2],[0,1,1,6],[0,6,6,7],[0,8,5,5],[1,4,4,8],[2,9,3,3],[3,9,9,8],[4,7,9,5],[6,8,7,7]]
PD code (use to draw this multiloop with SnapPy): [[10,7,1,8],[8,3,9,4],[4,9,5,10],[6,14,7,11],[1,15,2,20],[2,19,3,20],[5,12,6,11],[17,13,18,14],[15,18,16,19],[12,16,13,17]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (6,1,-7,-2)(8,5,-9,-6)(2,7,-3,-8)(15,20,-16,-17)(4,17,-5,-18)(18,3,-19,-4)(13,16,-14,-11)(10,11,-1,-12)(12,9,-13,-10)(19,14,-20,-15)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,6,-9,12)(-2,-8,-6)(-3,18,-5,8)(-4,-18)(-7,2)(-10,-12)(-11,10,-13)(-14,19,3,7,1,11)(-15,-17,4,-19)(-16,13,9,5,17)(-20,15)(14,16,20)
Multiloop annotated with half-edges
12^3_29 annotated with half-edges