$12^{1}_{293}$ - Minimal pinning sets
Pinning sets for 12^1_293 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_293 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, 5, 6, 9, 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, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,5,5],[0,6,6,7],[0,8,8,0],[1,8,7,5],[1,4,9,1],[2,9,9,2],[2,9,4,8],[3,7,4,3],[5,7,6,6]]
PD code (use to draw this loop with SnapPy): [[13,20,14,1],[12,5,13,6],[19,8,20,9],[14,2,15,1],[6,3,7,4],[4,11,5,12],[9,18,10,19],[7,16,8,17],[2,16,3,15],[17,10,18,11]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (4,1,-5,-2)(10,3,-11,-4)(17,6,-18,-7)(15,8,-16,-9)(2,9,-3,-10)(13,20,-14,-1)(5,14,-6,-15)(7,16,-8,-17)(11,18,-12,-19)(19,12,-20,-13)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,4,-11,-19,-13)(-2,-10,-4)(-3,10)(-5,-15,-9,2)(-6,17,-8,15)(-7,-17)(-12,19)(-14,5,1)(-16,7,-18,11,3,9)(-20,13)(6,14,20,12,18)(8,16)
Loop annotated with half-edges
12^1_293 annotated with half-edges