6,959 research outputs found
Genus Bounds for Harmonic Group Actions on Finite Graphs
This paper develops graph analogues of the genus bounds for the maximal size
of an automorphism group of a compact Riemann surface of genus .
Inspired by the work of M. Baker and S. Norine on harmonic morphisms between
finite graphs, we motivate and define the notion of a harmonic group action.
Denoting by M(g) the maximal size of such a harmonic group action on a graph of
genus , we prove that , and these bounds are
sharp in the sense that both are attained for infinitely many values of g.
Moreover, we show that the values and are the only values
taken by the function .Comment: 14 pages with 6 figures; section 8 rewritten to correct an error in
lemma 8.2; published versio
Construction of Negatively Curved Cubic Carbon Crystals via Standard Realizations
We constructed physically stable sp2 negatively curved cubic carbon
structures which reticulate a Schwarz P-like surface. The method for
constructing such crystal structures is based on the notion of the standard
realization of abstract crystal lattices. In this paper, we expound on the
mathematical method to construct such crystal structures
- β¦