$11^{3}_{10}$ - Minimal pinning sets
Pinning sets for 11^3_10 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^3_10 Pinning data
Pinning number of this multiloop: 5
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: 2.83846
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, 5, 7, 8}
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
6
2.39
7
0
0
15
2.67
8
0
0
20
2.88
9
0
0
15
3.04
10
0
0
6
3.17
11
0
0
1
3.27
Total
1
0
63
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 4, 4, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,4,5],[0,5,6,6],[0,6,7,0],[1,7,7,1],[1,8,8,2],[2,8,3,2],[3,8,4,4],[5,7,6,5]]
PD code (use to draw this multiloop with SnapPy): [[4,14,1,5],[5,11,6,10],[3,18,4,15],[13,1,14,2],[11,7,12,6],[9,15,10,16],[17,2,18,3],[12,7,13,8],[16,8,17,9]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (5,4,-6,-1)(18,3,-9,-4)(11,16,-12,-17)(17,12,-18,-13)(8,13,-5,-14)(15,10,-16,-11)(2,9,-3,-10)(1,6,-2,-7)(14,7,-15,-8)
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,-7,14,-5)(-2,-10,15,7)(-3,18,12,16,10)(-4,5,13,-18)(-6,1)(-8,-14)(-9,2,6,4)(-11,-17,-13,8,-15)(-12,17)(-16,11)(3,9)
Multiloop annotated with half-edges
11^3_10 annotated with half-edges