$12^{1}_{241}$ - Minimal pinning sets
Pinning sets for 12^1_241
Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_241
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, 3, 4, 7, 11}
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, 4, 4, 4, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,4,5,5],[0,6,7,0],[0,8,4,4],[1,3,3,8],[1,8,6,1],[2,5,9,9],[2,9,9,8],[3,7,5,4],[6,7,7,6]]
PD code (use to draw this loop with SnapPy): [[20,13,1,14],[14,3,15,4],[12,19,13,20],[1,6,2,7],[7,2,8,3],[15,5,16,4],[16,11,17,12],[18,9,19,10],[5,8,6,9],[10,17,11,18]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (5,20,-6,-1)(12,1,-13,-2)(2,13,-3,-14)(19,4,-20,-5)(3,6,-4,-7)(16,7,-17,-8)(14,9,-15,-10)(18,11,-19,-12)(8,15,-9,-16)(10,17,-11,-18)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,12,-19,-5)(-2,-14,-10,-18,-12)(-3,-7,16,-9,14)(-4,19,11,17,7)(-6,3,13,1)(-8,-16)(-11,18)(-13,2)(-15,8,-17,10)(-20,5)(4,6,20)(9,15)
Loop annotated with half-edges
12^1_241 annotated with half-edges