$12^{1}_{120}$ - Minimal pinning sets
Pinning sets for 12^1_120 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_120 Pinning data
Pinning number of this loop: 6
Total number of pinning sets: 80
of which optimal: 1
of which minimal: 2
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.91429
on average over minimal pinning sets: 2.22619
on average over optimal pinning sets: 2.16667
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 4, 5, 7, 11}
6
[2, 2, 2, 2, 2, 3]
2.17
a (minimal)
• {1, 2, 3, 4, 6, 7, 11}
7
[2, 2, 2, 2, 2, 3, 3]
2.29
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
2.17
7
0
1
6
2.47
8
0
0
19
2.73
9
0
0
26
2.94
10
0
0
19
3.12
11
0
0
7
3.25
12
0
0
1
3.33
Total
1
1
78
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 7, 8]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,3,3,4],[0,5,6,0],[0,4,1,1],[1,3,7,7],[2,8,9,6],[2,5,9,9],[4,8,8,4],[5,7,7,9],[5,8,6,6]]
PD code (use to draw this loop with SnapPy): [[3,20,4,1],[13,2,14,3],[19,4,20,5],[1,12,2,13],[14,12,15,11],[5,9,6,8],[18,7,19,8],[15,10,16,11],[9,16,10,17],[6,17,7,18]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,20,-12,-1)(17,2,-18,-3)(16,5,-17,-6)(6,3,-7,-4)(13,8,-14,-9)(9,12,-10,-13)(19,10,-20,-11)(7,14,-8,-15)(4,15,-5,-16)(1,18,-2,-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,-19,-11)(-2,17,5,15,-8,13,-10,19)(-3,6,-17)(-4,-16,-6)(-5,16)(-7,-15,4)(-9,-13)(-12,9,-14,7,3,-18,1)(-20,11)(2,18)(8,14)(10,12,20)
Loop annotated with half-edges
12^1_120 annotated with half-edges