journal articles
- Simplicial complexes with many facets are vertex decomposable,, with Ritika Nair, Jay Schweig, Adam Van Tuyl, and Russ Woodroofe, preprint, 10 pages.
- Simple homotopy for flag simplicial complexes and contractible transformations on graphs,, with Takahiro Matsushita, preprint, 6 pages, submitted (2023). Also on the ArXiv here.
- Chip-firing and parking functions on hypergraphs,, with Timothy Blanton, Isabelle Hong, Suho Oh, and Jenny Zhu, preprint, 15 pages.
- Shellability of the poset of lattice path matroid quotients,, with Carolina Benedetti, Kolja Knauer, and Yupeng Li, preprint, 15 pages.
- Chip-firing and critical groups of signed graphs, with Matthew Cho, Ryota Inagaki, Suho Oh, Dylan Snustad, and Bailee Zacovic, preprint, 31 pages, submitted (2023). Also on the ArXiv here.
- Root polytopes, tropical types, and toric edge ideals, with Ayah Almousa and Ben Smith, preprint, 45 pages, submitted (2022). Also on the ArXiv here.
- Homomorphism complexes, reconfiguration, and homotopy for directed graphs, with Anurag Singh, European Journal of Combinatorics 110 (2023). Also on the ArXiv here.
- Minimal graphs for contractible and dismantlable properties, with Jesus F. Espinoza, Martın E. Frıas-Armenta, and Hector A. Hernandez, Discrete Math. 346, Iss. 10 (2023). Also on the ArXiv here.
- Random subcomplexes and Betti numbers of random edge ideals, with Andrew Newman, International Mathematics Research Notices 2023, Iss. 10, pp. 8832–8871 (2023). Also on the ArXiv here.
- Completing and extending shellings of vertex decomposable complexes, with Michaela Coleman, Nathan Geist, and Suho Oh, SIAM Journal on Discrete Math 36, Iss. 2 (2022). Also on the ArXiv here.
- ntegral flow and cycle chip-firing on graphs, with Eli Meyers, Raghav Samavedam, and Alex Yi, Annals of Combinatorics 25(3), pp. 595–616 (2021). Also on the ArXiv here.
- Bi-coned graphs, edge-rooted forests, and h-vectors of matroid complexes, with Preston Cranford, Evan Haithcock, Joshua Marsh, Suho Oh, and Anna Truman, preprint 2020, 20 pages, Electronic Journal of Combinatorics 28(4) (2021), #P4.31. Also on the ArXiv here.
- Extendable shellability for d-dimensional complexes on d+3 vertices, with Jared Culbertson, Dan Guralnik, and Peter Stiller, Electronic Journal of Combinatorics 27(3) (2020). Also on the ArXiv here.
- Exposed circuits, linear quotients, and chordal clutters, Journal of Combinatorial Theory, Series A, 177 (2021). Also on the ArXiv here.
- Trees, parking functions, and standard monomials of skeleton ideals, with Weston King, Australasian Journal of Combinatorics 81(1), (2021), pp. 126–151. Also on the ArXiv here.
- One-skeleta of G-parking function ideals: resolutions and standard monomials, preprint 2016, 22 pages, submitted. Also on the ArXiv here.
- Warmth and connectivity of edge spaces of graphs, with Ragnar Freij, Advances in Applied Math, 96 (2018) pp. 176–194. Also on the ArXiv here.
- Face rings of cycles, associahedra, and standard tableaux, Electronic Journal of Combinatorics, Volume 23, Issue 3 (2016) . Also on the ArXiv here.
- Cellular resolutions from mapping cones, with Fatemeh Mohammadi, Journal of Combinatorial Theory, Series A, 128 (2014), pp. 180–206. Also on the ArXiv here.
- Laplacian ideals, arrangements, and resolutions, with Raman Sanyal, Journal of Algebra Combinatorics, 40, Issue 3 (2014), pp. 805–822. Also on the ArXiv here.
- Tropical types and associated cellular resolutions, with Michael Joswig and Raman Sanyal, Journal of Algebra, 356 (2012), pp. 304–324. Also on the ArXiv here.
- Cellular resolutions of cointerval ideals, with Alexander Engstrom, Mathematische Zeitschrift, Volume 270, Issue 1 (2012), pp. 145-163. Also on the ArXiv here.
- Algebraic properties of edge ideals via combinatorial topology, with Alexander Engstrom, Electronic Journal of Combinatorics, Volume 16, Issue 2 (2009) (The Björner Festschrift volume). Also on the ArXiv here.
- Topology of Hom complexes and test graphs for bounding chromatic number, with Carsten Schultz, Israel Journal of Mathematics 187, Issue 1 (2012), pp. 371–417. Also on the ArXiv here.
- Hom complexes and homotopy theory in the category of graphs, European Journal of Combinatorics 30, Number 2 (2009), pp. 490–509. Also on the ArXiv here.
- The universality of Hom complexes of graphs, Combinatorica 29, Iss. 4 (2009), pp. 433–448. Also on the ArXiv here.
- Homotopy groups of Hom complexes of graphs, Journal of Combinatorial Theory, Series A Volume 116, Issue 1 (2009), pp. 180–194. Also on the ArXiv here.
- Graphs with disjoint links in every spatial embedding , with Stephen Chan, Joel Foisy, Jennifer Hespen, Eman Kunz, Trent Lalonde, Quincy Loney, Katherine Sharrow, and Nathan Thomas, J. Knot Theory Ramifications 13 no. 6 (2004), pp. 737–748.
- Some linking properties of spatially embedded graphs (undergrad thesis), available here.
- Homomorphism complexes, reconfiguration, and homotopy for directed graphs, , with Anurag Singh, Formal Power Series and Algebraic Combinatorics (FPSAC) – DMTCS Proceedings (2022).
- Extending and completing shellings of vertex decomposable complexes, , with Michaela Coleman, Nathan Geist, and Suho Oh, Formal Power Series and Algebraic Combinatorics (FPSAC) – DMTCS Proceedings (2021).
- Hom complexes and homotopy in the category of graphs, , Electron. Notes Discrete Math., 31 (2008) pp. 131–136, The International Conference on Topological and Geometric Graph Theory.
conference proceedings
organizing
Chris Kapulkin, Antonio Rieser, and I will organize a special session on `Discrete homotopy theory’ at the JMM meeting to be held in San Francisco in January 2024.
Bennet Goeckner, Steve Klee, Gaku Liu, and I organized a special session on `Geometric and topological combinatorics’ held at the JMM meeting, originally scheduled to be held January 2022 in Seattle but postponed to April 2022 and held online due to Covid-19. More details can be found here.
Keri Sather-Wagstaff and I organized a special session on `Free Resolutions, Combinatorics, and Geometry’ as part of the AMS sectional meeting at the University of Texas at El Paso on September 12-13. More details can be found here.
Suho Oh and I organized a special session on `Geometric combinatorics and combinatorial commutative algebra’ as part of the AMS sectional meeting held at the University of North Texas on September 9-10. More details (including schedule of speakers) can be found here.
Together with Alex Engstrom and Tina O’Keefe I co-organized a special session on ‘Topological combinatorics and combinatorial commutative algebra’ as part of the AMS sectional meeting held at San Francisco State University, October 25-26, 2014. In addition we organized a one day satellite conference held (also) at SFSU on Friday, October 24. Click here for the Saturday/Sunday schedule and here for the Friday conference.
Together with Brant Jones, Matt Kahle, and Beth Kelly I helped organize the 2007 Graduate Student Combinatorics Conference, held at the U of Washington in Seattle on April 21-22, 2007. Check out the attractive conference poster here (warning: big file).
Other writings/songs
- A cognitive approach to the equivalence relation (under construction)
- Here is something I wrote for the Demonstrations project organized by artist Lun-Yi Tsai in Seattle in 2007.