$12^{1}_{223}$ - Minimal pinning sets
Pinning sets for 12^1_223 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_223 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, 4, 6, 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, 3, 4, 4, 4, 5, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,5,6],[0,6,6,7],[0,7,7,8],[0,9,9,5],[1,4,6,1],[1,5,2,2],[2,8,3,3],[3,7,9,9],[4,8,8,4]]
PD code (use to draw this loop with SnapPy): [[11,20,12,1],[17,10,18,11],[19,14,20,15],[12,5,13,6],[1,8,2,9],[9,16,10,17],[18,16,19,15],[4,13,5,14],[6,4,7,3],[7,2,8,3]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (5,20,-6,-1)(1,4,-2,-5)(10,3,-11,-4)(19,6,-20,-7)(15,8,-16,-9)(2,11,-3,-12)(17,12,-18,-13)(13,16,-14,-17)(7,14,-8,-15)(9,18,-10,-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,-5)(-2,-12,17,-14,7,-20,5)(-3,10,18,12)(-4,1,-6,19,-10)(-7,-15,-9,-19)(-8,15)(-11,2,4)(-13,-17)(-16,13,-18,9)(3,11)(6,20)(8,14,16)
Loop annotated with half-edges
12^1_223 annotated with half-edges