$11^{2}_{31}$ - Minimal pinning sets
Pinning sets for 11^2_31 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_31 Pinning data
Pinning number of this multiloop: 6
Total number of pinning sets: 32
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: 2.78769
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, 4, 5, 6}
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
5
2.4
8
0
0
10
2.7
9
0
0
10
2.93
10
0
0
5
3.12
11
0
0
1
3.27
Total
1
0
31
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 3, 3, 5, 5, 8]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,4,0],[0,5,6,3],[0,2,7,7],[1,5,5,1],[2,4,4,6],[2,5,8,8],[3,8,8,3],[6,7,7,6]]
PD code (use to draw this multiloop with SnapPy): [[8,18,1,9],[9,7,10,8],[12,17,13,18],[1,13,2,14],[6,10,7,11],[11,5,12,6],[16,4,17,5],[2,15,3,14],[3,15,4,16]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,2,-12,-3)(16,3,-17,-4)(14,5,-15,-6)(4,15,-5,-16)(7,18,-8,-9)(9,8,-10,-1)(1,10,-2,-11)(17,12,-18,-13)(6,13,-7,-14)
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)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,-11,-3,16,-5,14,-7,-9)(-2,11)(-4,-16)(-6,-14)(-8,9)(-10,1)(-12,17,3)(-13,6,-15,4,-17)(-18,7,13)(2,10,8,18,12)(5,15)
Multiloop annotated with half-edges
11^2_31 annotated with half-edges