$12^{1}_{239}$ - Minimal pinning sets
Pinning sets for 12^1_239 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_239 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, 4, 7, 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, 4, 4, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,2,0],[0,1,5,6],[0,6,6,7],[1,7,8,8],[2,8,9,9],[2,9,3,3],[3,9,8,4],[4,7,5,4],[5,7,6,5]]
PD code (use to draw this loop with SnapPy): [[5,20,6,1],[19,4,20,5],[6,4,7,3],[1,10,2,11],[18,13,19,14],[7,17,8,16],[9,2,10,3],[11,15,12,14],[12,17,13,18],[8,15,9,16]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (7,20,-8,-1)(1,4,-2,-5)(17,2,-18,-3)(19,8,-20,-9)(16,11,-17,-12)(12,9,-13,-10)(6,13,-7,-14)(14,5,-15,-6)(10,15,-11,-16)(3,18,-4,-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,-5,14,-7)(-2,17,11,15,5)(-3,-19,-9,12,-17)(-4,1,-8,19)(-6,-14)(-10,-16,-12)(-11,16)(-13,6,-15,10)(-18,3)(-20,7,13,9)(2,4,18)(8,20)
Loop annotated with half-edges
12^1_239 annotated with half-edges