$12^{2}_{278}$ - Minimal pinning sets
Pinning sets for 12^2_278 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_278 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, 3, 4, 9, 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, 4, 6, 8]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,5,5],[0,5,6,7],[0,7,7,0],[1,8,8,5],[1,4,2,1],[2,9,9,7],[2,6,3,3],[4,9,9,4],[6,8,8,6]]
PD code (use to draw this multiloop with SnapPy): [[14,20,1,15],[15,7,16,8],[17,13,18,14],[19,1,20,2],[6,9,7,10],[16,9,17,8],[12,3,13,4],[18,3,19,2],[10,5,11,6],[4,11,5,12]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,14,-10,-1)(7,2,-8,-3)(15,4,-16,-5)(5,16,-6,-17)(3,6,-4,-7)(1,8,-2,-9)(17,10,-18,-11)(19,12,-20,-13)(13,18,-14,-19)(11,20,-12,-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,-9)(-2,7,-4,15,-12,19,-14,9)(-3,-7)(-5,-17,-11,-15)(-6,3,-8,1,-10,17)(-13,-19)(-16,5)(-18,13,-20,11)(2,8)(4,6,16)(10,14,18)(12,20)
Multiloop annotated with half-edges
12^2_278 annotated with half-edges