A class of quadratic difference equations on a finite graph
Mathematical Physics
2011-09-16 v1 Combinatorics
math.MP
Abstract
We study a class of complex polynomial equations on a finite graph with a view to understanding how holistic phenomena emerge from combinatorial structure. Particular solutions arise from orthogonal projections of regular polytopes, invariant frameworks and cyclic sequences. A set of discrete parameters for which there exist non-trivial solutions leads to the construction of a polynomial invariant and the notion of a geometric spectrum. Geometry then emerges, notably dimension, distance and curvature, from purely combinatorial properties of the graph.
Cite
@article{arxiv.1109.3286,
title = {A class of quadratic difference equations on a finite graph},
author = {Paul Baird},
journal= {arXiv preprint arXiv:1109.3286},
year = {2011}
}