$12^{2}_{25}$ - Minimal pinning sets
Pinning sets for 12^2_25 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_25 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, 6, 7, 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, 4, 4, 4, 6, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,5,0],[0,6,6,7],[0,7,4,4],[1,3,3,7],[1,7,8,8],[2,9,9,2],[2,5,4,3],[5,9,9,5],[6,8,8,6]]
PD code (use to draw this multiloop with SnapPy): [[4,20,1,5],[5,3,6,4],[10,19,11,20],[1,14,2,13],[2,12,3,13],[6,15,7,16],[18,9,19,10],[11,15,12,14],[7,17,8,16],[8,17,9,18]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (14,1,-15,-2)(11,18,-12,-19)(4,5,-1,-6)(6,3,-7,-4)(7,20,-8,-5)(15,8,-16,-9)(9,16,-10,-17)(17,10,-18,-11)(19,12,-20,-13)(2,13,-3,-14)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,14,-3,6)(-2,-14)(-4,-6)(-5,4,-7)(-8,15,1,5)(-9,-17,-11,-19,-13,2,-15)(-10,17)(-12,19)(-16,9)(-18,11)(-20,7,3,13)(8,20,12,18,10,16)
Multiloop annotated with half-edges
12^2_25 annotated with half-edges