$11^{1}_{7}$ - Minimal pinning sets
Pinning sets for 11^1_7 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_7 Pinning data
Pinning number of this loop: 4
Total number of pinning sets: 128
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: 2.89692
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, 6, 10}
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
7
2.4
6
0
0
21
2.67
7
0
0
35
2.86
8
0
0
35
3.0
9
0
0
21
3.11
10
0
0
7
3.2
11
0
0
1
3.27
Total
1
0
127
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 6]
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],[1,3,6,7],[2,7,7,8],[2,8,8,4],[4,8,5,5],[5,7,6,6]]
PD code (use to draw this loop with SnapPy): [[3,18,4,1],[9,2,10,3],[17,4,18,5],[1,8,2,9],[10,8,11,7],[5,14,6,15],[16,11,17,12],[13,6,14,7],[15,13,16,12]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (7,18,-8,-1)(15,2,-16,-3)(11,4,-12,-5)(5,8,-6,-9)(17,6,-18,-7)(14,9,-15,-10)(10,13,-11,-14)(3,12,-4,-13)(1,16,-2,-17)
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,-17,-7)(-2,15,9,-6,17)(-3,-13,10,-15)(-4,11,13)(-5,-9,14,-11)(-8,5,-12,3,-16,1)(-10,-14)(-18,7)(2,16)(4,12)(6,8,18)
Loop annotated with half-edges
11^1_7 annotated with half-edges