2016/09/04 by S. C. Power, Power, Stephen C
Computer Science · Mathematics · #05C10 #05E99 #52C25 #82D25 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Mathematical Physics (math-ph) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1609.01275
openalex publication_date 2016/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A recent "hidden symmetry" conjecture of B. Gin-ge Chen et al is resolved, concerning the dimension of the mechanical modes of a generic 2-periodic triangulated surface O in R3 whose structure graph corresponds to a triangular tiling of R2. We introduce an indexing of the terms in an associated sparse determinant pO(z1, z2) by means of oriented 3-colourings of the underlying sparse graph, and use this and vertex splitting arguments to show that pO(z1,z2) is palindromic or antipalindromic, up to a shift index. This implies the conjectured dimension 1 phenomenon for these surfaces. As a corollary we obtain the topological stability of the generic modes of a 1-periodic triangulated nanotube.