On the entropy of spanning trees on a large triangular lattice
Abstract
Description
The double integral representing the entropy S_{tri} of spanning trees on a large triangular lattice is evaluated using two different methods, one algebraic and one graphical. Both methods lead to the same result S_{tri} = [1/(2 Pi)]^2 \int_0^{2 Pi} dθ\int_0^{2 Pi} dϕln [6-2 cos(θ) - 2 cos(ϕ) -2 cos(θ+ϕ)] = [3(\sqrt 3)/Pi](1 - 5^{-2} + 7^{-2} - 11^{-2} + 13^{-2} - ...)
16 pages, 3 figures, reference added, for Proceedings of the Gainesville Conference on Number Theory and Combinatorics in Physics, Ramanujan Journal
16 pages, 3 figures, reference added, for Proceedings of the Gainesville Conference on Number Theory and Combinatorics in Physics, Ramanujan Journal