Jeremy F. Alm

activity

20122026

most citedImproved bounds on the size of the smallest representation of relation algebra

3 2_{65}

4 citations · 16 across the 28 of their papers we have counts for

collaborators

32 papers

math.LO2026

Cyclic group representations for relation algebras $5 7_{65}$ and $6 3_{65}$

Jeremy F. Alm

We exhibit finite cyclic group representations for relation algebras $5 7_{65}$ and $6 3_{65}$ . As a consequence, of the ten symmetric integral RAs on four atoms having at least one…

math.LO2025

Relation Algebras Compatible with $Z_{2}$ -sets

Jeremy F. Alm, John W. Snow

We provide a characterization of those relation algebras which are isomorphic to the algebras of compatible relations of some $Z_{2}$ -set. We further prove that this class is finite…

math.LO2025

Monk Algebras and Representability

Jeremy F. Alm

In ``Monk Algebras and Ramsey Theory,'' \emph{J. Log. Algebr. Methods Program.} (2022), Kramer and Maddux prove various representability results in furtherance of the goal of findi…

math.CO2024

Chutes and Ladders: on some sequences inspired by 2017 Putnam A1

Jeremy F. Alm, Matt Salomone

The first problem of the 2017 Putnam competition was to characterize a set of natural numbers closed under both the square-root map $n^{2} \mapsto n$ and the "add 5 and square" map $…

math.LO2024

Cyclic Group Spectra for Some Small Relation Algebras

Jeremy F. Alm, Ashlee Bostic, Claire Chenault +2

The question of characterizing the (finite) representable relation algebras in a ``nice" way is open. The class $RRA$ is known to be not finitely axiomatizable in first-or…

math.LO2019★ 4 cited

Improved bounds on the size of the smallest representation of relation algebra $3 2_{65}$

Jeremy F. Alm, Michael Levet, Saeed Moazami +4

In this paper, we shed new light on the spectrum of the relation algebra we call $A_{n}$ , which is obtained by splitting the non-flexible diversity atom of $6_{7}$ into $n$ symmetr…

math.LO2019

Comer Schemes, Relation Algebras, and the Flexible Atom Conjecture

Jeremy F. Alm, David A. Andrews, Michael Levet

In this paper, we consider relational structures arising from Comer's finite field construction, where the cosets need not be sum free. These Comer schemes generalize the notion of…

math.NT2019

Arithmetic Progressions of Length Three in Multiplicative Subgroups of $F_{p}$

Jeremy F Alm

In this paper, we give an algorithm for detecting non-trivial 3-APs in multiplicative subgroups of $F_{p}^{\times}$ that is substantially more efficient than the naive approac…

math.LO2019★ 1 cited

Directed Ramsey and Anti-Ramsey Schemes and the Flexible Atom Conjecture

Jeremy F. Alm, Michael Levet

In this paper, we shed new light on the Flexible Atom Conjecture. We first give finite representation results for relation algebras $3 3_{37}, 3 5_{37}$ , $7 7_{83}$ , $7 8_{83}$ , $80_{8…

math.CO2018

Some Ordered Ramsey Numbers of Graphs on Four Vertices

Will Overman, Jeremy F. Alm, Kayla Coffey +1

An ordered graph $H$ on $n$ vertices is a graph whose vertices have been labeled bijectively with ${1, ..., n}$ . The ordered Ramsey number $r_{<} (H)$ is the minimum $n$ such that eve…

math.CO2018★ 1 cited

Random Relation Algebras

Jeremy F. Alm

We develop a random model for relation algebras. We prove some preliminary results and pose questions that lay out a new direction of research.

math.LO2017

Finite representations for two small relation algebras

Jeremy F. Alm, Roger D. Maddux

In this note, we give two different proofs that relation algebra $5 2_{65}$ is representable over a finite set. The first is probabilistic, and uses Johnson schemes. The second is a…

math.NT2017

2-Free Tetranacci Sequences

Jeremy F. Alm, Taylor Herald, Ellen Rammelkamp Miller +1

We consider a variant on the Tetranacci sequence, where one adds the previous four terms, then divides the sum by two until the result is odd. We give an algorithm for constructing…

math.CO2017

A fast coset-translation algorithm for computing the cycle structure of Comer relation algebras over $Z / p Z$

Jeremy F. Alm, Andrew Ylvisaker

Proper relation algebras can be constructed using $Z / p Z$ as a base set using a method due to Comer. The cycle structure of such an algebra must, in general, be de…

math.LO2017

Representability of Lyndon-Maddux relation algebras

Jeremy F. Alm

In Alm-Hirsch-Maddux (2016), relation algebras $L (q, n)$ were defined that generalize Roger Lyndon's relation algebras from projective lines, so that $L (q, 0)$ …

math.NT2016

401 and beyond: improved bounds and algorithms for the Ramsey algebra search

Jeremy F. Alm

In this paper, we discuss an improvement of an algorithm to search for primes $p$ and coset-partitions of Z/pZ* that yield Ramsey algebras over Z/pZ. We also prove an upper bound o…

physics.soc-ph2016

Degree-correlation, robustness, and vulnerability in finite scale-free networks

Jeremy F. Alm, Keenan M. L. Mack

Many naturally occurring networks have a power-law degree distribution as well as a non-zero degree correlation. Despite this, most studies analyzing the robustness to random node-…

math.LO2016

On sets of first-order formulas axiomatizing representable relation algebras

Jeremy F. Alm

This is the author's 2004 Master's thesis at Iowa State University, done under the supervision of Roger D. Maddux. It provides a background in relation algebras. Three results from…

math.CO2015

The vector graph and the chromatic number of the plane, or how NOT to prove that $χ (E^{2}) > 4$

Jeremy F. Alm, Jacob Manske

The chromatic number $χ (E^{2})$ of the plane is known to be some integer between 4 and 7, inclusive. We prove a limiting result that says, roughly, that one cann…

math.NT2015★ 1 cited

A Note on Prime Fibonacci Sequences

Jeremy Alm, Taylor Herald

In this paper, we define a variant of Fibonacci-like sequences that we call prime Fibonacci sequences, where one takes the sum of the previous two terms and returns the smallest od…

math.CO2015

A Reduced Upper Bound for an Edge-coloring Problem from Relation Algebra

Jeremy F. Alm, David A. Andrews

We construct an edge-coloring of $K_{N}$ (for $N = 3432$ ) in colors red, dark blue, and light blue, such that there are no monochromatic blue triangles and such that the coloring s…

math.CO2014

Generalizing $p$ -goodness to ordered graphs

Jeremy F. Alm, Patrick Bahls, Kayla Coffey +1

It is known that the connected graphs that are $p$ -good for all $p$ are the trees. In this paper, we ask which ordered trees are order- $p$ -good for all $p$ .

math.CO2014★ 1 cited

Mixed, Multi-color, and Bipartite Ramsey Numbers Involving Trees of Small Diameter

Jeremy F. Alm, Nicholas Hommowun, Aaron Schneider

In this paper we study Ramsey numbers for trees of diameter 3 (bistars) vs., respectively, trees of diameter 2 (stars), complete graphs, and many complete graphs. In the case of bi…

math.LO2013★ 3 cited

There is no finite-variable equational axiomatization of representable relation algebras over weakly representable relation algebras

Jeremy F. Alm, Robin Hirsch, Roger D. Maddux

We prove that any equational basis that defines RRA over wRRA must contain infinitely many variables. The proof uses a construction of arbitrarily large finite weakly representable…

Cyclic group representations for relation algebras 5765​ and 6365​

Relation Algebras Compatible with Z2​-sets

Monk Algebras and Representability

Chutes and Ladders: on some sequences inspired by 2017 Putnam A1

Cyclic Group Spectra for Some Small Relation Algebras

Improved bounds on the size of the smallest representation of relation algebra 3265​

Comer Schemes, Relation Algebras, and the Flexible Atom Conjecture

Arithmetic Progressions of Length Three in Multiplicative Subgroups of Fp​

Directed Ramsey and Anti-Ramsey Schemes and the Flexible Atom Conjecture

Some Ordered Ramsey Numbers of Graphs on Four Vertices

Random Relation Algebras

Finite representations for two small relation algebras

2-Free Tetranacci Sequences

A fast coset-translation algorithm for computing the cycle structure of Comer relation algebras over Z/pZ

Representability of Lyndon-Maddux relation algebras

401 and beyond: improved bounds and algorithms for the Ramsey algebra search

Degree-correlation, robustness, and vulnerability in finite scale-free networks

On sets of first-order formulas axiomatizing representable relation algebras

The vector graph and the chromatic number of the plane, or how NOT to prove that χ(E2)>4

A Note on Prime Fibonacci Sequences

A Reduced Upper Bound for an Edge-coloring Problem from Relation Algebra

Generalizing p-goodness to ordered graphs

Mixed, Multi-color, and Bipartite Ramsey Numbers Involving Trees of Small Diameter

There is no finite-variable equational axiomatization of representable relation algebras over weakly representable relation algebras

Cyclic group representations for relation algebras $5 7_{65}$ and $6 3_{65}$

Relation Algebras Compatible with $Z_{2}$ -sets

Improved bounds on the size of the smallest representation of relation algebra $3 2_{65}$

Arithmetic Progressions of Length Three in Multiplicative Subgroups of $F_{p}$

A fast coset-translation algorithm for computing the cycle structure of Comer relation algebras over $Z / p Z$

The vector graph and the chromatic number of the plane, or how NOT to prove that $χ (E^{2}) > 4$

Generalizing $p$ -goodness to ordered graphs