John R. Schmitt

activity

20122025

most citedMartin Gardner's minimum no-3-in-a-line problem

4 citations · 6 across the 7 of their papers we have counts for

collaborators

9 papers

math.CO2025

Structured and Punctured Nullstellensätze

Erhard Aichinger, John R. Schmitt, Henry Zhan

A Nullstellensatz is a theorem providing information on polynomials that vanish on a certain set: David Hilbert's Nullstellensatz (1893) is a cornerstone of algebraic geometry, and…

math.CO2024

Repeatedly applying the Combinatorial Nullstellensatz for Zero-sum Grids to Martin Gardner's minimum no-3-in-a-line problem

Seunghwan Oh, John R. Schmitt, Xianzhi Wang

In 1976 Martin Gardner posed the following problem: ``What is the smallest number of [queens] you can put on an [ $n \times n$ chessboard] such that no [queen] can be added without…

math.CO2022

Higher Degree Erdos-Ginzburg-Ziv Constants

Yair Caro, John R. Schmitt

We generalize the notion of Erdős-Ginzburg-Ziv constants -- along the same lines we generalized in earlier work the notion of Davenport constants -- to a ``higher degree" and obtai…

math.CO2021

Growable Realizations: a Powerful Approach to the Buratti-Horak-Rosa Conjecture

M. A. Ollis, Anita Pasotti, Marco A. Pellegrini +1

Label the vertices of the complete graph $K_{v}$ with the integers ${0, 1, \dots, v - 1}$ and define the length of the edge between $x$ and $y$ to be $min (∣ x - y ∣, v - ∣ x - y ∣)$ .…

math.CO2021★ 1 cited

Higher Degree Davenport Constants over Finite Commutative Rings

Yair Caro, Benjamin Girard, John R. Schmitt

We generalize the notion of Davenport constants to a `higher degree' and obtain various lower and upper bounds, which are sometimes exact as is the case for certain finite commutat…

math.CO2018

Distinct Partial Sums in Cyclic Groups: Polynomial Method and Constructive Approaches

Jacob Hicks, M. A. Ollis, John. R. Schmitt

Let $(G, +)$ be an abelian group and consider a subset $A \subseteq G$ with $∣ A ∣ = k$ . Given an ordering $(a_{1}, \dots, a_{k})$ of the elements of $A$ , define its {\em partial sums} by…

math.CO2015

On zeros of a polynomial in a finite grid

Anurag Bishnoi, Pete L. Clark, Aditya Potukuchi +1

A 1993 result of Alon and Füredi gives a sharp upper bound on the number of zeros of a multivariate polynomial over an integral domain in a finite grid, in terms of the degree of t…

math.NT2014★ 1 cited

Warning's Second Theorem with Resricted Variables

Pete L. Clark, Aden Forrow, John R. Schmitt

We present a restricted variable generalization of Warning's Second Theorem (a result giving a lower bound on the number of solutions of a low degree polynomial system over a finit…

math.CO2012★ 4 cited

Martin Gardner's minimum no-3-in-a-line problem

Alec S. Cooper, Oleg Pikhurko, John R. Schmitt +1

In Martin Gardner's October, 1976 Mathematical Games column in Scientific American, he posed the following problem: "What is the smallest number of [queens] you can put on a board…