I plan to write some notes on dynamical algebraic combinatorics (perhaps to one day be converted into a book). You can see the tentative outline here.
(Links below are to journal versions, but all of my papers are available on the arXiv.)
Dynamical algebraic combinatorics
- Symmetry of Narayana numbers and rowvacuation of root posets, with Colin Defant. Forum of Mathematics, Sigma, 9, 2021.
- The birational Lalanne-Kreweras involution, with Michael Joseph. Algebraic Combinatorics, 5(2), 2022.
- Order polynomial product formulas and poset dynamics. Preprint, 2020, arXiv:2006.01568. For the AMS volume on Open Problems in Algebraic Combinatorics, to accompany the 2022 conference at UMN.
- Promotion of Kreweras words, with Martin Rubey. Selecta Mathematica (N.S.) 28(1), 2022.
- Cyclic sieving for plane partitions and symmetry. SIGMA Symmetry Integrability Geom. Methods Appl., 16, 2020.
Expectations of combinatorial statistics
- Homomesy via toggeleability statistics, with Colin Defant, Svetlana Poznanović, and James Propp. Preprint, 2021, arxiv:2108.13227.
- Minuscule doppelgängers, the coincidental down-degree expectations property, and rowmotion. Preprint, 2019, arXiv:1902.07301. To appear in Experimental Mathematics.
- The CDE property for skew vexillary permutations. Journal of Combinatorial Theory, Series A, 168, 2019.
- The CDE property for minuscule lattices. Journal of Combinatorial Theory, Series A, 152, 2017.
- The expected jaggedness of order ideals, with Melody Chan, Shahrzad Haddadan, and Luca Moci. Forum of Mathematics, Sigma, 5, 2017.
- A note on statistical averages for oscillating tableaux, with Ingrid Zhang. Electronic Journal of Combinatorics, 22(2), 2015.
Enumeration of plane partitions
- On the q-enumeration of barely set-valued tableaux and plane partitions, with Alexander Lazar and Svante Linusson. Preprint, 2021, arXiv:2106.07418.
- Plane partitions of shifted double staircase shape, with Tri Lai. Journal of Combinatorial Theory, Series A, 183, 2021.
Labeled chip-firing and root system chip-firing
- A positive formula for the Ehrhart-like polynomials from root system chip-firing, with Alexander Postnikov. Algebraic Combinatorics, 2(6), 2019.
- Root system chip-firing II: Central-firing, with Pavel Galashin, Thomas McConville, and Alexander Postnikov. International Mathematics Research Notices, 2021, no. 13.
- Root system chip-firing I: Interval-firing, with Pavel Galashin, Thomas McConville, and Alexander Postnikov. Mathematische Zeitschrift, 292(3-4), 2019.
- Sorting via chip-firing, with Thomas McConville and James Propp. Electronic Journal of Combinatorics, 24(3), 2017.
Parking functions, graph orientations and the Tutte polynomial
- Fourientation activities and the Tutte polynomial, with Spencer Backman and Lorenzo Traldi. European Journal of Combinatorics, 67, 2018.
- Fourientations and the Tutte polynomial, with Spencer Backman. Research in the Mathematical Sciences, 4, 2017.
- Parking functions and tree inversions revisited, with Petar Gaydarov. Advances in Applied Mathematics, 80, 2016.
- Bigraphical arrangements, with David Perkinson. Transactions of the American Mathematical Society, 368(1), 2016.
- Another proof of Wilmes' conjecture. Discrete Mathematics, 323, 2014.
- Orientations, semiorders, arrangements, and parking functions, with David Perkinson. Electronic Journal of Combinatorics, 19(4), 2012.
- A note on Möbius functions of upho posets. Preprint, 2022, arxiv:2202.12103.
- Quantum integer-valued polynomials, with Nate Harman. Journal of Algebraic Combinatorics, 45(2), 2017.
- Interlacing networks: birational RSK, the octahedron recurrence, and Schur function identities with Miriam Farber and Wuttisak Trongsiriwat. Journal of Combinatorial Theory, Series A, 133, 2015.
- Pattern avoidance in poset permutations, with Morgan Weiler. Order, 33(2), 2016.
Talk slides & other miscellanea
- Slides from my 2022 talk on the rank and characteristic generating functions of upper homogeneous posets at the University of Minnesota combinatorics seminar.
- Slides from my 2021 talk on promotion, webs, and plabic graphs at the BIRS workshop on dynamical algebraic combiantorics.
- Crux - The Last Problem: Demystified, an expository article for the problem journal Crux Mathematicorum contextualizing a problem from their June 2021 issue.
- Slides from my 2020 talk on order polynomial product formulas and poset dynamics at the University of Minnesota combinatorics seminar.
- Slides from my 2018 talk on root system chip-firing at FPSAC, Dartmouth.
- Problems from the 2015 CMO-BIRS sandpile workshop.
- Notes from the 2015 AIM workshop on dynamical algebraic combinatorics.
- Slides from my 2014 talk on bigraphical arrangements at FPSAC, Chicago.
- RSK via local transformations, an expository article based on MIT combinatorics preseminar presentations of Alex Postnikov, 2014.
- Problems from the 2013 AIM workshop on chip-firing.
Open access journals in combinatorics
There are several online, open access journals in combinatorics. I especially like:
- The Electronic Journal of Combinatorics
- Algebraic Combinatorics ("flipped" from Journal of Algebraic Combinatorics)
- Combinatorial Theory ("flipped" from Journal of Combinatorial Theory: Series A)