David A. Nash

activity

20142020

collaborators

6 papers

math.GR2020

Classifying groups with a small number of subgroups

David A. Nash, Alexander Betz

We provide lower bounds on the number of subgroups of a group $G$ as a function of the primes and exponents appearing in the prime factorization of $∣ G ∣$ . Using these bounds, we cl…

math.HO2019

A New Take on Classic 'Pen Problems'

David A. Nash

In this article we generalize the classic "farm pen" optimization problem from a first course in calculus in a handful of different ways. We describe the solution to an $n$ -dimensi…

math.CO2018

Non-magic Hypergraphs

Benjamin Ellis, David A. Nash, Jonathan Needleman +1

This article studies a generalization of magic squares to $k$ -uniform hypergraphs. In traditional magic squares the entries come from the natural numbers. A magic labeling of the v…

math.CO2017

Minimal and maximal Numbrix puzzles

Mary Grace Hanson, David A. Nash

This paper explores special arrangements of clues in $m \times n$ Numbrix puzzles. The maximum number of clues which fails to define an $m \times n$ puzzle is demonstrated for all…

math.CO2015

When are finite projective planes magic?

David Nash, Jonathan Needleman

This article studies a generalization of magic squares to finite projective planes. In traditional magic squares the entries come from the natural numbers. This does not work for f…

math.RT2014

On Magic Finite Projective Space

David Nash, Jonathan Needleman

This paper studies a generalization of magic squares to finite projective space $P^{n} (q)$ . We classify at all functions from $P^{n} (q)$ into a finite field where the…