$12^{1}_{302}$ - Minimal pinning sets
Pinning sets for 12^1_302 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_302 Pinning data
Pinning number of this loop: 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, 6, 7, 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 loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 4, 4, 5, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,2],[0,3,4,0],[0,5,6,0],[1,6,7,7],[1,7,5,5],[2,4,4,8],[2,9,9,3],[3,8,4,3],[5,7,9,9],[6,8,8,6]]
PD code (use to draw this loop with SnapPy): [[5,20,6,1],[19,4,20,5],[6,2,7,1],[18,11,19,12],[3,16,4,17],[2,16,3,15],[7,13,8,12],[10,17,11,18],[14,9,15,10],[13,9,14,8]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (16,1,-17,-2)(5,10,-6,-11)(11,6,-12,-7)(15,8,-16,-9)(9,4,-10,-5)(12,19,-13,-20)(20,13,-1,-14)(7,14,-8,-15)(2,17,-3,-18)(18,3,-19,-4)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,16,8,14)(-2,-18,-4,9,-16)(-3,18)(-5,-11,-7,-15,-9)(-6,11)(-8,15)(-10,5)(-12,-20,-14,7)(-13,20)(-17,2)(-19,12,6,10,4)(1,13,19,3,17)
Loop annotated with half-edges
12^1_302 annotated with half-edges