$12^{1}_{7}$ - Minimal pinning sets
Pinning sets for 12^1_7 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_7 Pinning data
Pinning number of this loop: 4
Total number of pinning sets: 256
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: 2.96564
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, 5, 11}
4
[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
4
1
0
0
2.0
5
0
0
8
2.4
6
0
0
28
2.67
7
0
0
56
2.86
8
0
0
70
3.0
9
0
0
56
3.11
10
0
0
28
3.2
11
0
0
8
3.27
12
0
0
1
3.33
Total
1
0
255
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,4,5],[0,6,6,7],[0,7,8,8],[0,5,1,1],[1,4,9,6],[2,5,7,2],[2,6,9,3],[3,9,9,3],[5,8,8,7]]
PD code (use to draw this loop with SnapPy): [[3,20,4,1],[2,15,3,16],[19,8,20,9],[4,11,5,12],[1,17,2,16],[17,14,18,15],[9,18,10,19],[10,7,11,8],[5,13,6,12],[6,13,7,14]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (8,5,-9,-6)(17,6,-18,-7)(2,9,-3,-10)(10,3,-11,-4)(4,11,-5,-12)(15,12,-16,-13)(20,13,-1,-14)(14,19,-15,-20)(7,16,-8,-17)(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,-19,14)(-2,-10,-4,-12,15,19)(-3,10)(-5,8,16,12)(-6,17,-8)(-7,-17)(-9,2,18,6)(-11,4)(-13,20,-15)(-14,-20)(-16,7,-18,1,13)(3,9,5,11)
Loop annotated with half-edges
12^1_7 annotated with half-edges