$12^{2}_{1}$ - Minimal pinning sets

Minimal pinning semi-lattice

(y-axis: cardinality)

Pinning data

• Pinning number of this multiloop: 10
• Total number of pinning sets: 4
• 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: 2.69697
  • on average over minimal pinning sets: 2.0
  • on average over optimal pinning sets: 2.0

Refined data for the minimal pinning sets

Data for pinning sets in each cardinal

Other information about this multiloop

Properties

• Region degree sequence: [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10]
• Minimal region degree: 2
• Is multisimple: Yes

Combinatorial encoding data

• Plantri embedding: [[1,1,2,2],[0,3,3,0],[0,4,4,0],[1,5,5,1],[2,6,6,2],[3,7,7,3],[4,8,8,4],[5,9,9,5],[6,9,9,6],[7,8,8,7]]
• PD code (use to draw this multiloop with SnapPy): [[10,20,1,11],[11,9,12,10],[19,1,20,2],[8,12,9,13],[2,18,3,19],[13,7,14,8],[17,3,18,4],[6,14,7,15],[4,16,5,17],[15,5,16,6]]
• Permutation representation (action on half-edges):
  • Vertex permutation $\sigma=$ (20,1,-11,-2)(18,3,-19,-4)(16,5,-17,-6)(14,7,-15,-8)(12,9,-13,-10)(6,15,-7,-16)(4,17,-5,-18)(2,19,-3,-20)(10,11,-1,-12)(8,13,-9,-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)(-19,19)(-20,20)
  • Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,20,-3,18,-5,16,-7,14,-9,12)(-2,-20)(-4,-18)(-6,-16)(-8,-14)(-10,-12)(-11,10,-13,8,-15,6,-17,4,-19,2)(1,11)(3,19)(5,17)(7,15)(9,13)

Multiloop annotated with half-edges