$12^{1}_{290}$ - Minimal pinning sets
Pinning sets for 12^1_290 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_290 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, 3, 4, 5, 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, 4, 7, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,5,5],[0,5,6,6],[0,7,4,0],[1,3,7,5],[1,4,2,1],[2,8,8,2],[3,9,9,4],[6,9,9,6],[7,8,8,7]]
PD code (use to draw this loop with SnapPy): [[9,20,10,1],[8,13,9,14],[19,6,20,7],[10,2,11,1],[14,11,15,12],[12,7,13,8],[5,18,6,19],[2,16,3,15],[17,4,18,5],[16,4,17,3]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (20,13,-1,-14)(14,1,-15,-2)(16,3,-17,-4)(9,4,-10,-5)(11,8,-12,-9)(5,10,-6,-11)(12,19,-13,-20)(2,15,-3,-16)(6,17,-7,-18)(18,7,-19,-8)
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)(-2,-16,-4,9,-12,-20,-14)(-3,16)(-5,-11,-9)(-6,-18,-8,11)(-7,18)(-10,5)(-13,20)(-15,2)(-17,6,10,4)(-19,12,8)(1,13,19,7,17,3,15)
Loop annotated with half-edges
12^1_290 annotated with half-edges