$12^{1}_{296}$ - Minimal pinning sets
Pinning sets for 12^1_296 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_296 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, 3, 6, 9}
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, 3, 5, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,4,2],[0,1,5,5],[0,6,7,0],[1,7,8,1],[2,8,9,2],[3,9,7,7],[3,6,6,4],[4,9,9,5],[5,8,8,6]]
PD code (use to draw this loop with SnapPy): [[20,5,1,6],[6,13,7,14],[14,19,15,20],[4,1,5,2],[12,7,13,8],[18,15,19,16],[2,10,3,9],[3,8,4,9],[11,16,12,17],[17,10,18,11]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (18,3,-19,-4)(10,5,-11,-6)(1,6,-2,-7)(7,20,-8,-1)(15,8,-16,-9)(4,11,-5,-12)(16,13,-17,-14)(9,14,-10,-15)(12,17,-13,-18)(2,19,-3,-20)
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,-7)(-2,-20,7)(-3,18,-13,16,8,20)(-4,-12,-18)(-5,10,14,-17,12)(-6,1,-8,15,-10)(-9,-15)(-11,4,-19,2,6)(-14,9,-16)(3,19)(5,11)(13,17)
Loop annotated with half-edges
12^1_296 annotated with half-edges