Equal Lagrange Numbers with Non-Isomorphic Band Graphs: A Counterexample to Schiffler's Problem 6.3
Year: 2026
Type: preprint
Abstract: We consider the following question: if two lattice paths in the same set $\mathcal{D}(a,b)$ have the same Lagrange number, must their band graphs be isomorphic? We exhibit two explicit lattice paths in $\mathcal{D}(17,9)$ with the same Lagrange number but non-isomorphic associated band graphs, thereby giving a counterexample to this question.
Source: arXiv (Cornell University)
Authors: Tang, Qiyue, Zhang, Yizhi
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203946285