Over the last decade, I have worked on projects in knot theory, combinatorial game theory, and algebraic and enumerative combinatorics. I am currently working on a variety of projects that fall under the banner of computational combinatorics. My work involves a fair amount of programming with Sage to see if ideas are backed up by data, followed by rigorous proofs to establish general theorems.
For more information on past and future research, please see my research statement.
Scientific Writing
Preprints
Cost-sharing in Parking Games, J.E., Pamela E. Harris, Jan Kretschmann, J. Carlos Martínez Mori. Preprint available on the arXiv.
Toggling, rowmotion, and homomesy on interval-closed sets, J.E., Nadia Lafrenière, Erin McNicholas, Jessica Striker, Amanda Welch. To appear in Journal of Combinatorics, preprint available on the arXiv.
Boolean Intervals in the Weak Order of Sn, J.E., Pamela E. Harris, Jan Kretschmann, J. Carlos Martínez Mori. Preprint available on the arXiv. Slides from AMS Sectional available here:
Flattened Stirling Permutations, Adam Buck, J.E., Azia A. Figueroa, Pamela E. Harris, Kimberly Harry, Anthony Simpson. Preprint available on the arXiv. Extended Abstract from Permutation Patterns 2023, page 72.
Graphs of Sets of Reduced Words, J.E. Preparing for journal submission, preprint available on the arXiv.
Publications
Homomesies on permutations, J.E., Nadia Lafrenière, Erin McNicholas, Jessica Striker, Amanda Welch. Published in Mathematics of Computation in 2023.
On Flattened Parking Functions, J.E., Pamela E. Harris, Zoe Markman, Izah Tahir, Amanda Verga. Published in Journal of Integer Sequences in 2023. Extended Abstract from Permutation Patterns 2023, page 58.
A Note on the Factorization of Permutations into Cycles, J.E., Oscar Vega. Published in the International Electronic Journal of Algebra in 2017.
Combinatorial Analysis of a Subtraction Game on Graphs, Richard Adams, Janae Dixon, J.E., Jamie Peabody, Oscar Vega, Karen Willis. Published in the International Journal of Combinatorics in 2016.
On Invariants for Spatial Graphs, Elaina Aceves, J.E. Published in the Rose Hulman Undergraduate Mathematics Journal in 2015.
Copies of my dissertation, Graphs of Sets of Reduced Words, are available through the ASU Library, and copies of my master’s thesis, Generalizations of the Futurama Theorem, are available through the Fresno State Library. Both are also available upon request.
Work with Students
In summer 2022, I worked with the Summer@ICERM program. Over the course of the eight-week program I assisted the organizers with managing the various teams of undergraduates as they worked on projects related to parking functions. This program is gave me an inside look at the various procedures for a summer research experience: everything from how the applications for funding are written, selection of projects suitable for undergraduates, the organization of the summer, how to determine student strengths and select research groups, and other aspects of mathematical development. My primary group consisted of three undergraduates, who worked with me under the supervision of organizer Pamela Harris. I have also collaborated with a second group from the Summer@ICERM program over the course of the 2022-23 academic year.
In addition to the summer program, I have supervised three undergraduate honors projects at Rockhurst University, and I have been collaborating with graduate students at UW Milwaukee. The work done with these students is forthcoming.
Fellowships and Grants (2021-Present)
A complete list of travel grants and research fellowships can be found in my CV.
- June 2023 – AWM Mentorship Travel Grant with Pamela E. Harris ($5000)
- March 2023 – Gems of Combinatorics at American Institute of Mathematics (AIM) – Funding from AIM (for travel)
- January 2023 – Primarily Undergraduate Institute Travel Grant for Joint Math Meetings – Funding from AMS ($1050)
- January 2023 – Collaberate@ICERM – Funding from ICERM (for travel)
- 2022-2023 – Home For All DEI Program Fellowship – Funding from Rockhurst University ($500)
- 2021-2022 – Research Community in Algebraic Combinatorics – Funding from ICERM (Fellowship of $1250, plus additional travel funding)
- Summer 2021 – Graduate Student Summer Research Block Grant – Funding from ASU ($5000)
Presentations (2021-Present)
A complete list of conference presentations, seminar, and colloquia can be found in my CV.
- Oct. 7, 2023 – Finding Needles in Haystacks @ AMS Fall Central Sectional Meeting
- May 5, 2023 – Homomesy of Permutations Colloquium @ UW Milwaukee
- May 3, 2023 – Fun and Games with Tableaux Keynote @ WI Math Council Annual Conference 2023
- May 2, 2023 – Integer Sequences and Parking Functions Algebra Seminar @ UW Milwaukee
- April 17, 2023 – Integer Sequences and Parking Functions @ Truman State
- April 10, 2023 – Integer Sequences and Parking Functions @ Kenyon College
- Feb. 6, 2023 – Integer Sequences and Parking Functions @ Sacramento State
- Jan. 6, 2023 – Graphs of Sets of Reduced Words @ JMM 2023
- July 19, 2022 – Twelve Months of Permutations @ ICERM
- July 12, 2022 – Website Panel @ ICERM
- July 5, 2022 – CV Writing Panel @ ICERM
- June 13, 2022 – Posets and Permutations Intro Lectures @ ICERM
- Feb. 10, 2022 – Dynamical Algebraic Combinatorics @ ICERM
- Dec. 3, 2021 – Graphs of Sets of Reduced Words Colloquium @ Fresno State
- Oct. 1, 2021 – Graphs of Sets of Reduced Words @ University of Kansas
- Apr. 14, 2021 – Graphs of Sets of Reduced Words @ Arizona State University
Student Research Documents
As detailed in my research statement, I have several projects set aside for students. Below is a document I have prepared as an introduction to posets, permutations, and pattern avoidance.
An updated document specifically for permutations is available below.