$12^{1}_{153}$ - Minimal pinning sets
Pinning sets for 12^1_153 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_153 Pinning data
Pinning number of this loop: 7
Total number of pinning sets: 48
of which optimal: 2
of which minimal: 2
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.86152
on average over minimal pinning sets: 2.14286
on average over optimal pinning sets: 2.14286
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 4, 5, 6, 7, 11}
7
[2, 2, 2, 2, 2, 2, 3]
2.14
B (optimal)
• {1, 2, 3, 5, 6, 7, 11}
7
[2, 2, 2, 2, 2, 2, 3]
2.14
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
7
2
0
0
2.14
8
0
0
9
2.53
9
0
0
16
2.82
10
0
0
14
3.04
11
0
0
6
3.21
12
0
0
1
3.33
Total
2
0
46
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 3, 3, 5, 5, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,4,5,6],[0,7,7,0],[0,5,8,8],[1,9,9,5],[1,4,3,6],[1,5,7,7],[2,6,6,2],[3,9,9,3],[4,8,8,4]]
PD code (use to draw this loop with SnapPy): [[20,9,1,10],[10,5,11,6],[8,19,9,20],[1,12,2,13],[15,4,16,5],[11,16,12,17],[6,17,7,18],[18,7,19,8],[2,14,3,13],[3,14,4,15]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (13,2,-14,-3)(8,3,-9,-4)(16,5,-17,-6)(18,7,-19,-8)(19,10,-20,-11)(11,20,-12,-1)(1,12,-2,-13)(9,14,-10,-15)(4,15,-5,-16)(6,17,-7,-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,-13,-3,8,-19,-11)(-2,13)(-4,-16,-6,-18,-8)(-5,16)(-7,18)(-9,-15,4)(-10,19,7,17,5,15)(-12,1)(-14,9,3)(-17,6)(-20,11)(2,12,20,10,14)
Loop annotated with half-edges
12^1_153 annotated with half-edges