$12^{1}_{294}$ - Minimal pinning sets
Pinning sets for 12^1_294 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_294 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 128
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: 2.90623
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, 5, 8, 9}
5
[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
5
1
0
0
2.0
6
0
0
7
2.38
7
0
0
21
2.65
8
0
0
35
2.86
9
0
0
35
3.02
10
0
0
21
3.14
11
0
0
7
3.25
12
0
0
1
3.33
Total
1
0
127
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 3, 3, 5, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,5,5],[0,6,6,7],[0,8,8,0],[1,9,9,5],[1,4,6,1],[2,5,7,2],[2,6,9,8],[3,7,9,3],[4,8,7,4]]
PD code (use to draw this loop with SnapPy): [[20,15,1,16],[16,5,17,6],[19,10,20,11],[14,1,15,2],[4,7,5,8],[17,7,18,6],[11,18,12,19],[12,9,13,10],[2,13,3,14],[8,3,9,4]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (5,20,-6,-1)(13,2,-14,-3)(3,14,-4,-15)(1,4,-2,-5)(9,6,-10,-7)(16,7,-17,-8)(19,10,-20,-11)(17,12,-18,-13)(8,15,-9,-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,-5)(-2,13,-18,11,-20,5)(-3,-15,8,-17,-13)(-4,1,-6,9,15)(-7,16,-9)(-8,-16)(-10,19,-12,17,7)(-11,-19)(-14,3)(2,4,14)(6,20,10)(12,18)
Loop annotated with half-edges
12^1_294 annotated with half-edges