$12^{2}_{3}$ - Minimal pinning sets

Minimal pinning semi-lattice

(y-axis: cardinality)

Pinning data

• Pinning number of this multiloop: 8
• Total number of pinning sets: 16
• 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: 2.76717
  • 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, 6, 6, 6, 6]
• Minimal region degree: 2
• Is multisimple: Yes

Combinatorial encoding data

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

Multiloop annotated with half-edges