11 citations · 23 across the 23 of their papers we have counts for
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Geodesic Bases for Lie Algebras
Grant Cairns, Ana Hinić Galić, Yuri Nikolayevsky +1
For finite dimensional real Lie algebras, we investigate the existence of an inner product having a basis comprised of geodesic elements. We give several existence and non-existenc…
A sharp refinement of a result of Zverovich--Zverovich
Grant Cairns, Stacey Mendan, Yuri Nikolayevsky
For a finite sequence of positive integers to be the degree sequence of a finite graph, Zverovich and Zverovich gave a sufficient condition involving only the length of the sequenc…
An improvement of a result of Zverovich--Zverovich
Grant Cairns, Stacey Mendan
We give an improvement of a result of Zverovich and Zverovich which gives a condition on the first and last elements in a decreasing sequence of positive integers for the sequence…
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.