33 citations · 43 across the 8 of their papers we have counts for
8 papers
A survey of Heffter arrays
A. Pasotti, J. H. Dinitz
Heffter arrays were introduced by Archdeacon in 2015 as an interesting link between combinatorial designs and topological graph theory. Since the initial paper on this topic, there…
Seeds for Generalized Taxicab Numbers
Jeffrey. H. Dinitz, Richard Games, Robert Roth
The generalized taxicab number is equal to the smallest number that is the sum of positive th powers in ways. This definition is inspired by Ramanujan's obser…
Tight Heffter Arrays Exist for all Possible Values: The Research Report
Dan S. Archdeacon, Tomas Boothby, Jeffrey H. Dinitz
A tight Heffter array H(m,n) is an m x n matrix with nonzero entries from Z_{2mn+1} such that i) the sum of the elements in each row and each column is 0, and ii) no element from {…
Biembedding Steiner Triple Systems and n-cycle Systems on Orientable Surfaces
Jeffrey H. Dinitz, Amelia R. W. Mattern
In 2015, Archdeacon introduced the notion of Heffter arrays and showed the connection between Heffter arrays and biembedding m-cycle and an n-cycle systems on a surface. In this pa…
On Partial Sums in Cyclic Groups
D. S. Archdeacon, J. H. Dinitz, A. Mattern +1
We are interested in ordering the elements of a subset A of the non-zero integers modulo n in such a way that all the partial sums are distinct. We conjecture that this can always…
Square Integer Heffter Arrays with Empty Cells
D. S. Archdeacon, J. H. Dinitz, D. M. Donovan +1
A Heffter array is an matrix with nonzero entries from such that each row contains filled cells and each column contains …