$10^{2}_{11}$ - Minimal pinning sets
Pinning sets for 10^2_11 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^2_11 Pinning data
Pinning number of this multiloop: 4
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: 2.8189
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, 4, 7}
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
6
2.4
6
0
0
15
2.67
7
0
0
20
2.86
8
0
0
15
3.0
9
0
0
6
3.11
10
0
0
1
3.2
Total
1
0
63
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 3, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,3,2,0],[0,1,4,4],[0,5,5,1],[2,6,7,2],[3,7,6,3],[4,5,7,7],[4,6,6,5]]
PD code (use to draw this multiloop with SnapPy): [[8,16,1,9],[9,7,10,8],[10,15,11,16],[1,6,2,7],[14,11,15,12],[5,2,6,3],[12,5,13,4],[13,3,14,4]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,8,-10,-1)(1,16,-2,-9)(6,3,-7,-4)(13,4,-14,-5)(2,7,-3,-8)(10,15,-11,-16)(14,11,-15,-12)(5,12,-6,-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)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,-9)(-2,-8,9)(-3,6,12,-15,10,8)(-4,13,-6)(-5,-13)(-7,2,16,-11,14,4)(-10,-16,1)(-12,5,-14)(3,7)(11,15)
Multiloop annotated with half-edges
10^2_11 annotated with half-edges