4 papers
Some Remarks on Graphical Sequences for Graphs and Bipartite Graphs
Grant Cairns, Stacey Mendan
For finite sequence $\underbar{\em d}$ of positive integers, we consider graphs that have $\underbar{\em d}$ as their list of vertex degrees, and bipartite graphs for which each pa…
Morley's other miracle: $\displaystyle 4^{p-1}\equiv\pm (\smallmatrix p-1 \frac{p-1}{2} \endsmallmatrix) \pmod {p^3} $
Christian Aebi, Grant Cairns
Frank Morley is famous for his theorem concerning the angle trisectors of a triangle. This note gives an elementary proof of another result of Morley's, which relates the middle bi…
Wilson Theorems for Double-, Hyper-, Sub- and Super-factorials
Christian Aebi, Grant Cairns
We present generalisations of Wilson's theorem for double factorials, hyperfactorials, subfactorials and superfactorials.
On the existence of orthonormal geodesic bases for Lie algebras
Grant Cairns, Nguyen Thanh Tung Le, Anthony Nielsen +1
We show that every unimodular Lie algebra, of dimension at most 4, equipped with an inner product, possesses an orthonormal basis comprised of geodesic elements. On the other hand,…