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The U-B color has been suggested as a predictor of the presence of water of hydration on asteroids. Photometry from the Eight-Color Asteroid Survey was used to test this concept. An overlap in U-B colors prevents this magnitude difference from distinguishing between surface material that was thermally processed at higher temperatures and surface material that was aqueously altered. Two tests of the presence of water of hydration using visible spectral region photometry failed to flag those few higher albedo M- and E-class asteroids having photometry that shows a 3.0-μm water of hydration absorption. These asteroids probably contain little or no oxidized iron in their surface material. We develop combinatorial methods for establishing lower bounds on the rotation distance between binary trees, i.e. , equivalently, on the flip distance between triangulations of a polygon. These methods lead to sharp estimates for certain particular Beats Solo Sale Canada pairs of trees. As an application, we prove that, for each Beats By Dre Toronto n , there exist size n trees at distance <img height="17" border="0" style="vertical-align:bottom" width="84" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0001870809003107-si1.gif">2n−O(n), i.e., the diameter of the nth associahedron has at least this value.