$12^{1}_{32}$ - Minimal pinning sets
Pinning sets for 12^1_32 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_32 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, 6, 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: [[1,1,2,3],[0,4,4,0],[0,5,3,3],[0,2,2,6],[1,6,5,1],[2,4,7,8],[3,8,7,4],[5,6,9,9],[5,9,9,6],[7,8,8,7]]
PD code (use to draw this loop with SnapPy): [[20,3,1,4],[4,19,5,20],[11,2,12,3],[1,12,2,13],[18,5,19,6],[10,17,11,18],[13,7,14,6],[14,9,15,10],[16,7,17,8],[8,15,9,16]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,20,-10,-1)(18,1,-19,-2)(16,3,-17,-4)(4,11,-5,-12)(14,5,-15,-6)(12,7,-13,-8)(19,10,-20,-11)(6,13,-7,-14)(8,15,-9,-16)(2,17,-3,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,18,-3,16,-9)(-2,-18)(-4,-12,-8,-16)(-5,14,-7,12)(-6,-14)(-10,19,1)(-11,4,-17,2,-19)(-13,6,-15,8)(-20,9,15,5,11)(3,17)(7,13)(10,20)
Loop annotated with half-edges
12^1_32 annotated with half-edges