Kean Fallon

collaborators

3 papers

math.CO2023

Rainbow numbers of $[m] \times [n]$ for $x_{1} + x_{2} = x_{3}$

Kean Fallon, Ethan Manhart, Joe Miller +3

Consider the set $[m] \times [n] = {(i, j) : 1 \leq i \leq m, 1 \leq j \leq n}$ and the equation $x_{1} + x_{2} = x_{3}$ , namely $e q$ . The \emph{rainbow number of $[m] \times [n]$ for $e q$ }, d…

math.CO2019

Counterexamples to Siegel's Conjecture

Kean P. Fallon, Madisyn Janusiak, Edward D. Kim +1

We prove that the intersection of a Hirsch polytope and a cube may be a non-Hirsch polytope.

math.CO2019

Rainbow numbers of $[n]$ for $\sum_{i = 1}^{k - 1} x_{i} = x_{k}$

Kean Fallon, Colin Giles, Hunter Rehm +2

Consider the set ${1, 2, \dots, n} = [n]$ and an equation $e q$ . The rainbow number of $[n]$ for $e q$ , denoted $rb ([n], e q)$ , is the smallest number of colors such that…

Rainbow numbers of [m]×[n] for x1​+x2​=x3​

Counterexamples to Siegel's Conjecture

Rainbow numbers of [n] for ∑i=1k−1​xi​=xk​

Rainbow numbers of $[m] \times [n]$ for $x_{1} + x_{2} = x_{3}$

Rainbow numbers of $[n]$ for $\sum_{i = 1}^{k - 1} x_{i} = x_{k}$