$11^{1}_{92}$ - Minimal pinning sets
Pinning sets for 11^1_92 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_92 Pinning data
Pinning number of this loop: 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, 4, 5, 8, 10}
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 loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 3, 3, 6, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,4,2],[0,1,5,5],[0,6,6,0],[1,7,7,1],[2,8,8,2],[3,8,7,3],[4,6,8,4],[5,7,6,5]]
PD code (use to draw this loop with SnapPy): [[18,11,1,12],[12,5,13,6],[6,17,7,18],[10,1,11,2],[4,13,5,14],[16,7,17,8],[2,9,3,10],[14,3,15,4],[8,15,9,16]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (12,1,-13,-2)(10,3,-11,-4)(14,5,-15,-6)(18,7,-1,-8)(16,9,-17,-10)(2,11,-3,-12)(6,13,-7,-14)(4,15,-5,-16)(8,17,-9,-18)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,12,-3,10,-17,8)(-2,-12)(-4,-16,-10)(-5,14,-7,18,-9,16)(-6,-14)(-8,-18)(-11,2,-13,6,-15,4)(1,7,13)(3,11)(5,15)(9,17)
Loop annotated with half-edges
11^1_92 annotated with half-edges