$12^{1}_{24}$ - Minimal pinning sets
Pinning sets for 12^1_24 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_24 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, 3, 3, 5, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,3,3,4],[0,5,6,0],[0,4,1,1],[1,3,6,5],[2,4,7,8],[2,9,9,4],[5,9,8,8],[5,7,7,9],[6,8,7,6]]
PD code (use to draw this loop with SnapPy): [[3,20,4,1],[11,2,12,3],[19,4,20,5],[1,10,2,11],[12,10,13,9],[5,9,6,8],[18,13,19,14],[6,15,7,16],[16,7,17,8],[14,17,15,18]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,20,-10,-1)(17,2,-18,-3)(14,5,-15,-6)(6,3,-7,-4)(7,10,-8,-11)(19,8,-20,-9)(16,11,-17,-12)(4,13,-5,-14)(12,15,-13,-16)(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,-9)(-2,17,11,-8,19)(-3,6,-15,12,-17)(-4,-14,-6)(-5,14)(-7,-11,16,-13,4)(-10,7,3,-18,1)(-12,-16)(-20,9)(2,18)(5,13,15)(8,10,20)
Loop annotated with half-edges
12^1_24 annotated with half-edges