Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
On Enumeration Of Conjugacy Classes Of Coxeter Elements, Matthew Macauley, Henning S. Mortveit
On Enumeration Of Conjugacy Classes Of Coxeter Elements, Matthew Macauley, Henning S. Mortveit
Publications
In this paper we study the equivalence relation on the set of acyclic orientations of a graph Y that arises through source-to-sink conversions. This source-to-sink conversion encodes, e.g. conjugation of Coxeter elements of a Coxeter group. We give a direct proof of a recursion for the number of equivalence classes of this relation for an arbitrary graph Y using edge deletion and edge contraction of non-bridge edges. We conclude by showing how this result may also be obtained through an evaluation of the Tutte polynomial as T (Y, 1, 0), and we provide bijections to two other classes of acyclic …
Geodesic Flow On Global Holomorphic Sections Of Ts2, Brendan Guilfoyle, Wilhelm Klingenberg
Geodesic Flow On Global Holomorphic Sections Of Ts2, Brendan Guilfoyle, Wilhelm Klingenberg
Publications
We study the geodesic flow on the global holomorphic sections of the bundle π : TS2 → S 2 induced by the neutral K¨ahler metric on the space of oriented lines of R 3 , which we identify with TS2 . This flow is shown to be completely integrable when the sections are symplectic, and the behaviour of the geodesics is described.
Geodesic Flow On The Normal Congruence Of A Minimal Surface, Brendan Guilfoyle, Wilhelm Klingenberg
Geodesic Flow On The Normal Congruence Of A Minimal Surface, Brendan Guilfoyle, Wilhelm Klingenberg
Publications
We study the geodesic flow on the normal line congruence of a minimal surface in ℝ3 induced by the neutral Kähler metric on the space of oriented lines. The metric is lorentz with isolated degenerate points and the flow is shown to be completely integrable. In addition, we give a new holomorphic description of minimal surfaces in ℝ3 and relate it to the classical Weierstrass representation.