2025/05/07 by Pallavi Panda, Panda, Pallavi, Hugo Parlier +3
Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2505.04074
openalex publication_date 2025/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a surface Σ with punctures that serve as marked points and at least one marked point on each boundary component. We build a filling surface Σn by singling out one of the boundary components and denoting by n the number of marked points it contains. We consider the triangulations of Σn whose vertices are the marked points and the associated flip-graph F(Σn). Quotienting F(Σn) by the homeomorphisms of Σ that fix the privileged boundary component results in a finite graph MF(Σn). Bounds on the diameter of MF(Σn) are available when Σ is orientable and we provide corresponding bounds when Σ is non-orientable. We show that the diameter of this graph grows at least like 5n/2 and at most like 4n as n goes to infinity. If Σ is an unpunctured Möbius strip, MF(Σn) coincides with F(Σn) and we prove that the diameter of this graph grows exactly like 5n/2 as n goes to infinity.