Recent botanical collections by H. S. McKee and Douglas E. Yen, together with the few available records from published papers, have been collated into a checklist of the known vascular plants of the Horne and Wallis Islands. Of 248 species here listed, 170 appear to be indigenous. Many of these are widespread, but 45 of them are limited to the Fijian Region (New Hebrides to Samoa) . Of the four...

We explore criteria that data must meet in order for the Kruskal-Wallis test to reject the null hypothesis by computing the number of unique ranked 1 data sets in the balanced case where each of the m alternatives has n observations. We show that the Kruskal-Wallis test tends to be conservative in rejecting the null hypothesis, and we offer a correction that improves its performance. We then co...

We present examples of flag homology spheres whose γvectors satisfy the Kruskal-Katona inequalities. This includes several families of well-studied simplicial complexes, including Coxeter complexes and the simplicial complexes dual to the associahedron and to the cyclohedron. In another direction, we show that if a flag (d− 1)-sphere has at most 2d + 2 vertices its γ-vector satisfies the Kruska...