$12^{1}_{303}$ - Minimal pinning sets
Pinning sets for 12^1_303 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_303 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, 4, 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, 3, 3, 4, 5, 6, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,5,0],[0,6,6,3],[0,2,7,7],[1,8,9,9],[1,9,6,6],[2,5,5,2],[3,8,8,3],[4,7,7,9],[4,8,5,4]]
PD code (use to draw this loop with SnapPy): [[13,20,14,1],[19,12,20,13],[14,10,15,9],[1,9,2,8],[18,5,19,6],[11,16,12,17],[10,16,11,15],[2,7,3,8],[6,3,7,4],[4,17,5,18]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (4,1,-5,-2)(16,3,-17,-4)(20,5,-1,-6)(6,19,-7,-20)(7,12,-8,-13)(17,10,-18,-11)(13,8,-14,-9)(9,14,-10,-15)(2,15,-3,-16)(11,18,-12,-19)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,4,-17,-11,-19,6)(-2,-16,-4)(-3,16)(-5,20,-7,-13,-9,-15,2)(-6,-20)(-8,13)(-10,17,3,15)(-12,7,19)(-14,9)(-18,11)(1,5)(8,12,18,10,14)
Loop annotated with half-edges
12^1_303 annotated with half-edges