$12^{1}_{313}$ - Minimal pinning sets
Pinning sets for 12^1_313 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_313 Pinning data
Pinning number of this loop: 6
Total number of pinning sets: 64
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: 2.85421
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, 3, 5, 6, 9, 11}
6
[2, 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
6
1
0
0
2.0
7
0
0
6
2.38
8
0
0
15
2.67
9
0
0
20
2.89
10
0
0
15
3.07
11
0
0
6
3.21
12
0
0
1
3.33
Total
1
0
63
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 3, 4, 4, 5, 5, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,5,5],[0,6,6,7],[0,7,7,0],[1,8,8,5],[1,4,6,1],[2,5,9,2],[2,9,3,3],[4,9,9,4],[6,8,8,7]]
PD code (use to draw this loop with SnapPy): [[20,15,1,16],[16,8,17,7],[12,19,13,20],[14,1,15,2],[8,5,9,6],[17,6,18,7],[18,11,19,12],[13,3,14,2],[4,9,5,10],[10,3,11,4]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (3,20,-4,-1)(12,1,-13,-2)(2,11,-3,-12)(19,4,-20,-5)(13,6,-14,-7)(15,10,-16,-11)(7,14,-8,-15)(9,16,-10,-17)(17,8,-18,-9)(5,18,-6,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,12,-3)(-2,-12)(-4,19,-6,13,1)(-5,-19)(-7,-15,-11,2,-13)(-8,17,-10,15)(-9,-17)(-14,7)(-16,9,-18,5,-20,3,11)(4,20)(6,18,8,14)(10,16)
Loop annotated with half-edges
12^1_313 annotated with half-edges