Logan Crew

Here is a list of pairs of small graphs that have equal chromatic symmetric function, and their characteristics. This list was compiled by myself and Sophie Spirkl with a computer program, using the database of graphs provided by Brendan McKay on his homepage.

My wife Sophie Spirkl is an Assistant Professor in the Department of Combinatorics & Optimization at the University of Waterloo.

Students:

PhD -  Josephine Reynes (2021-) [co-supervised with Karen Yeats]

Masters - Evan Haithcock (2021-2023), Laura Pierson (2023-2024) [co-supervised with Oliver Pechenik]

Undergraduate - William Chan (2021), Yongxing (Nick) Zhang (2022), Michael Xu (2023)

Preprints:

• 1. The Kromatic Symmetric Function: A K-Theoretic Analogue with Oliver Pechenik and Sophie Spirkl. Submitted (2023).

• 2. e-basis Coefficients of Chromatic Symmetric Functions with Yongxing Zhang. Submitted (2022).

Published and accepted papers:

1. On Prime Cayley Graphs with Maria Chudnovsky, Michal Cizek, Ján Mináč, Tung Nguyen, Sophie Spirkl, and Nguyên Tân. 

Accepted by Journal of Combinatorics (2025).

2. Homogeneous Sets in Graphs and a Chromatic Multisymmetric Function with Evan Haithcock, Josephine Reynes, and Sophie Spirkl.

Published by Advances in Applied Mathematics (2024).

3. A Graph Polynomial from Chromatic Symmetric Functions with William Chan.

Published by Journal of Graph Theory (2023).

4.  Plethysms of Chromatic and Tutte Symmetric Functions with Sophie Spirkl. 

Published by Electronic Journal of Combinatorics (2022).

5. A Note on Distinguishing Trees with the Chromatic Symmetric Function. 

Published by Discrete Mathematics (2022).

6.  Modular Relations of the Tutte Symmetric Function with Sophie Spirkl. 

Published by Journal of Combinatorial Theory, Series A (2022).

7. Branching Rules for Splint Root Systems with Alexandre A. Kirillov and Yao-Rui Yeo. 

Published by Journal of Algebras and Representation Theory (2022).

8. A Vertex-Weighted Tutte Symmetric Function, and Constructing Graphs with Equal Chromatic Symmetric Function with José Aliste-Prieto, Sophie Spirkl, and José Zamora. 

Published by Electronic Journal of Combinatorics (2021).

9. A Complete Multipartite Basis for the Chromatic Symmetric Function with Sophie Spirkl. 

Published by SIAM Journal on Discrete Mathematics (SIDMA) (2021).

10. Disproportionate Division with Bhargav Narayanan and Sophie Spirkl. 

Published by Bulletin of the London Mathematical Society (2020).

11. A Deletion-Contraction Relation for the Chromatic Symmetric Function with Sophie Spirkl.  

Published by European Journal of Combinatorics (2020).

Talks/Presentations:

• 1. The Kromatic Symmetric Function (Poster). Conference on Formal Power Series and Algebraic Combinatorics (FPSAC) (2023).

• 2. The Kromatic Symmetric Function (Slides). UC Davis Algebraic Geometry Seminar (2023)

• 3. The Kromatic Symmetric Function. Rutgers University Schubert Seminar (2023).

• 4. Chromatic Symmetric Functions: How to Study Graphs using Algebra, and Vice Versa (slides). Western University Special Seminar (2023).

• 5. Chromatic Multisymmetric Functions. York University Applied Algebra Seminar (2022).

• 6. A Graph Theoretic Approach to Plethysms of Symmetric Functions. University of Waterloo Algebraic Combinatorics Seminar (2022).

• 7. Graph Bases from the Chromatic Symmetric Function (Slides). AMS Western Sectional Meeting, Special Session on Graph Colorings (2022).

• 8. The Chromatic Symmetric Function: A Refinement of the Chromatic Polynomial (Slides). Illinois Institute of Technology Discrete Math Seminar (2022).

• 9. Graph Polynomials from Chromatic Symmetric Functions (Video/Slides). NTNU Algebraic and Combinatorial Perspectives in the Mathematical Sciences Seminar (2022).

• 10. A New Graph Polynomial from the Chromatic Symmetric Function (Slides Here). University of Waterloo Algebraic Graph Theory Seminar (2021).

• 11. Structural Properties of the Chromatic and Tutte Symmetric Functions (Slides Only). University of British Columbia Discrete Math Seminar (2021).

• 12. Identities of the Chromatic and Tutte Symmetric Functions (Slides Only). Canadian Discrete and Algorithmic Mathematics Conference (CanaDAM, 2021).

• 13. The Tutte Symmetric Function (Slides Only). University of Waterloo Tutte Colloquium (2020).

• 14. Edge Deletion-Contraction in the Chromatic and Tutte Symmetric Functions. York University Applied Algebra Seminar (2020). (Slides)

• 15. Edge Deletion-Contraction in the Chromatic and Tutte Symmetric Functions. University of Waterloo Algebraic Combinatorics Seminar (2020).

• 16. Edge Deletion-Contraction in the Chromatic and Tutte Symmetric Functions. University of Florida Combinatorics Seminar (2020).

• 17. A Deletion-Contraction Relation for the Chromatic Symmetric Function (and Slides). University of Albany Virtual Discrete Math 2-Day (2020).

• 18. A Deletion-Contraction Relation for the Chromatic Symmetric Function (Slides Only). Canadian Discrete and Algorithmic Mathematics Conference (CanaDAM, 2019).

Teaching:

Spring 2023: MATH239 and CO480 (see below)

Winter 2023: MATH239 (Introduction to Combinatorics)

Spring 2022: CO380 (Mathematical Discovery and Invention)

Winter 2022: MATH119 (Calculus 2 for Engineering)

Spring 2021: CO480 (History of Mathematics)

Winter 2021: MATH228 (Differential Equations for Physics and Chemistry)

Fall 2020: MATH115 (Linear Algebra for Engineering)

Reviewer for:

Mathematical Reviews, Advances in Mathematics, International Math Research Notices, Journal of Graph Theory, Advances in Applied Mathematics, Annals of Combinatorics, Discrete Mathematics, and Discrete Applied Mathematics.

PhD thesis: 

Vertex-Weighted Generalizations of Chromatic Symmetric Functions. Advisors: Jim Haglund and Greta Panova (University of Pennsylvania, 2020).

Master's thesis: 

The Shuffle Conjecture. Advisor: Jim Haglund (University of Pennsylvania, 2017).

Bachelor's thesis: 

On the characterization of the numbers n such that any group of order n has a given property P. Advisor: Thomas Haines (University of Maryland, College Park, 2015).