Sam Hopkins
samuelfhopkins@gmail.com
Selected research papers
Dynamical algebraic combinatorics
Symmetry of Narayana numbers and rowvacuation of root posets , with Colin Defant. Preprint, 2021, arXiv:2101.02329.
The birational Lalanne-Kreweras involution , with Michael Joseph. Preprint, 2020, arXiv:2012.15795.
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. Preprint, 2020, arXiv:2005.14031.
Cyclic sieving for plane partitions and symmetry . SIGMA Symmetry Integrability Geom. Methods Appl., 16, 2020.
Enumeration of plane partitions
q-Enumeration of barely set-valued tableaux and plane partitions , with Alexander Lazar and Svante Linusson. In preparation, 2021.
Plane partitions of shifted double staircase shape , with Tri Lai. Preprint, 2020, arXiv:2007.05381. To appear in Journal of Combinatorial Theory, Series A.
Expectations of combinatorial statistics
Homomesy via toggeleability statistics , with Colin Defant, Svetlana Poznanović, and James Propp. In preparation, 2021.
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.
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. Preprint, 2017, arXiv:1708.04849. To appear in International Mathematics Research Notices.
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.
Graph orientations and the Tutte polynomial
Parking functions
Other mathematical writing
Slides from my 2020 talk on order polynomial product formulas and poset dynamics at the University of Minnesota combinatorics seminar.
Slides from my 2019 talk on the coincidental down-degree expectations (CDE) phenomenon at the LaCIM combinatorics seminar.
Slides from my 2017 talk on root system chip-firing at the University of Minnesota combinatorics seminar.
Problems from the 2015 CMO-BIRS sandpile workshop.
Slides from my 2015 talk on fourientations and the Tutte polynomial at the Cornell probability seminar.
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.