7 citations · 8 across the 8 of their papers we have counts for
9 papers
On the equivalence of Playfair's axiom to the parallel postulate
Elizabeth T. Brown, Emily Castner, Stephen Davis +3
We show that the classical equivalence of Euclid's parallel postulate and Playfair's axiom collapses in the absence of triangle congruence. In particular, we construct a non-SAS ge…
The Refined Lecture Hall Theorem via Abacus Diagrams
Laura Bradford, Meredith Harris, Brant Jones +3
Bousquet-Mélou & Eriksson's lecture hall theorem generalizes Euler's celebrated distinct-odd partition theorem. We present an elementary and transparent proof of a refined version…
Bachet's Problem: as few weights to weigh them all
Edwin O'Shea
A problem that enjoys an enduring popularity asks: "what is the least number of pound weights that can be used on a scale pan to weigh any integral number of pounds from 1 to 40 in…
Relaxed complete partitions: an error-correcting Bachet's problem
Jorge Bruno, Edwin O'Shea
Motivated by an error-correcting generalization of Bachet's weights problem, we define and classify relaxed complete partitions. We show that these partitions enjoy a succinct desc…
On the occurrence of large gaps in small contingency tables
Edwin O'Shea
Examples of small contingency tables on binary random variables with large integer programming gaps on the lower bounds of cell entries were constructed by Sullivant. We argue here…
Ehrhart clutters: Regularity and Max-Flow Min-Cut
Jose Martinez-Bernal, Edwin O'Shea, Rafael H. Villarreal
If C is a clutter with n vertices and q edges whose clutter matrix has column vectors V={v1,...,vq}, we call C an Ehrhart clutter if {(v1,1),...,(vq,1)} is a Hilbert basis. Letting…