11 citations · 23 across the 23 of their papers we have counts for
5 papers · 1 filter
Equitable Candy Sharing
Grant Cairns
Children, sitting in a circle, each have a nonnegative number of candies in front of them. A whistle is blown and each child with more than one candy passes one candy to the left a…
A sufficient condition for a pair of sequences to be bipartite graphic
Grant Cairns, Stacey Mendan, Yuri Nikolayevsky
We present a sufficient condition for a pair of finite integer sequences to be degree sequences of a bipartite graph, based only on the lengths of the sequences and their largest a…
Sums of Quadratic residues and nonresidues
Christian Aebi, Grant Cairns
It is well known that when a prime is congruent to 1 modulo 4, the sum of the quadratic residues equals the sum of the quadratic nonresidues. In this note we give analogous res…
Curvature properties of metric nilpotent Lie algebras which are independent of metric
G. Cairns, A. Hinić Galić, Y. Nikolayevsky
This paper consists of two parts. First, motivated by classic results, we determine the subsets of a given nilpotent Lie algebra (respectively, of the Grassmannian o…
Wolstenholme again
Christian Aebi, Grant Cairns
We give an elementary and self-contained proof of the equivalence of a collection of Wolstenholme-type congruences due to Helou and Terjanian.