$12^{2}_{283}$ - Minimal pinning sets
Pinning sets for 12^2_283 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_283 Pinning data
Pinning number of this multiloop: 7
Total number of pinning sets: 32
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: 2.80821
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, 8, 9, 11}
7
[2, 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
7
1
0
0
2.0
8
0
0
5
2.4
9
0
0
10
2.71
10
0
0
10
2.96
11
0
0
5
3.16
12
0
0
1
3.33
Total
1
0
31
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 2, 3, 5, 6, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,4,0],[0,5,6,6],[0,7,8,8],[1,5,5,1],[2,4,4,8],[2,9,9,2],[3,9,9,8],[3,7,5,3],[6,7,7,6]]
PD code (use to draw this multiloop with SnapPy): [[6,20,1,7],[7,5,8,6],[10,19,11,20],[1,16,2,15],[4,8,5,9],[9,3,10,4],[18,11,19,12],[16,13,17,14],[2,14,3,15],[12,17,13,18]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (16,1,-17,-2)(14,3,-15,-4)(2,15,-3,-16)(11,18,-12,-19)(9,20,-10,-7)(6,7,-1,-8)(8,5,-9,-6)(19,10,-20,-11)(17,12,-18,-13)(4,13,-5,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,16,-3,14,-5,8)(-2,-16)(-4,-14)(-6,-8)(-7,6,-9)(-10,19,-12,17,1,7)(-11,-19)(-13,4,-15,2,-17)(-18,11,-20,9,5,13)(3,15)(10,20)(12,18)
Multiloop annotated with half-edges
12^2_283 annotated with half-edges