Dynamical Algebraic Combinatorics

Publications (by subtopic)

This is an incomplete list of papers in the area, though we aim to make it comprehensive. If you know of a paper in the area of dynamical algebraic combinatorics to add to this list, please complete this form. If you'd like to help edit the webpage, please email jessica.striker@ndsu.edu.

Survey Papers:

• Order polynomial product formulas and poset dynamics, by Sam Hopkins. In Open Problems in Algebraic Combinatorics, Proceedings of Symposia in Pure Mathematics (2024).

• Dynamical algebraic combinatorics: promotion, rowmotion, and resonance, by Jessica Striker. Notices of the AMS (2017).

• Dynamical Algebraic Combinatorics and the Homomesy Phenomenon, by Tom Roby. In Recent Trends in Combinatorics, Springer (2016).

• What is... Cyclic Sieving?, by Vic Reiner, Dennis Stanton, and Dennis White. Notices of the AMS (2014).

Promotion:

• Toric promotion with reflections and refractions, by Ashleigh Adams, Colin Defant, and Jessica Striker, (preprint). 

• Identifying orbit lengths for promotion, by Elise Catania, Jack Kendrick, Heather M. Russell, and Julianna Tymoczko, (preprint). 

• On the Order of P-Strict Promotion on V x [l], by Ben Adenbaum. Electronic Journal of Combinatorics (2025).

• Promotion permutations for tableaux, by Christian Gaetz, Oliver Pechenik, Stephan Pfannerer, Jessica Striker, and Joshua P. Swanson, Combinatorial Theory (2024).

• P-strict promotion and Q-partition rowmotion: the graded case, by Joseph Bernstein, Jessica Striker, and Corey Vorland, European Journal of Combinatorics (2024).

• Curious cyclic sieving on increasing tableaux, by Christian Gaetz, Oliver Pechenik, Jessica Striker, and Joshua P. Swanson, Enumerative Combinatorics and Applications (2022).

• Promotion of Kreweras words, by Sam Hopkins and Martin Rubey. Selecta Mathematica (2022).

• Minuscule analogues of the plane partition periodicity conjecture of Cameron and Fon-Der-Flaass, by Oliver Pechenik, Combinatorial Theory (2022).

• P-strict promotion and B-bounded rowmotion, with applications to tableaux of many flavors, by Joseph Bernstein, Jessica Striker, and Corey Vorland, Combinatorial Theory (2021).

• Dynamics of plane partitions: Proof of the Cameron–Fon-Der-Flaass conjecture, by Rebecca Patrias and Oliver Pechenik, Forum of Mathematics Sigma (2020).

• Promotion on generalized oscillating tableaux and web rotation, by Rebecca Patrias, JCTA (2019).

• Rowmotion and increasing labeling promotion, by Kevin Dilks, Jessica Striker, and Corey Vorland, Journal of Combinatorial Theory Series A (2019).

• Orbits of plane partitions of exceptional Lie type, by Holly Mandel and Oliver Pechenik, European Journal of Combinatorics (2018).

• Promotion of increasing tableaux: Frames and homomesies, by Oliver Pechenik, Electronic Journal of Combinatorics (2017).

• Resonance in orbits of plane partitions and increasing tableaux, by Kevin Dilks, Jessica Striker, and Oliver Pechenik, Journal of Combinatorial Theory Series A (2017).

• Proofs and generalizations of a homomesy conjecture of Propp and Roby, by Jonathan Bloom, Oliver Pechenik, and Dan Saracino, Discrete Mathematics (2016).

• Increasing tableaux, Narayana numbers and an instance of the cyclic sieving phenomenon, by T. Pressey, A. Stokke, and T.I. Visentin, Annals of Combinatorics (2016).

• Jeu-de-taquin promotion and a cyclic sieving phenomenon for semistandard hook tableaux, by M. Bennett, B.W. Madill, and A. Stokke, Discrete Mathematics (2014).

• Cyclic sieving of increasing tableaux and small Schröder paths, by Oliver Pechenik, Journal of Combinatorial Theory Series A (2014).

• Promotion and evacuation, by Richard P. Stanley, Electronic Journal of Combinatorics (2009).

Toggling and Rowmotion:

• Interval-closed set rowmotion and homomesy on products of two chains, by Nadia Lafrenière, Joel Brewster Lewis, Erin McNicholas, Jessica Striker, and Amanda Welch (preprint).

• Rowmotion on the chain of V's poset and whirling dynamics, by Matthew Plante and Tom Roby (preprint).

• Rowmotion on rooted trees, by Pranjal Dangwal, Jamie Kimble, Jinting Liang, Jianzhi Lou, Bruce E. Sagan, Zach Stewart (preprint).

• Plane partitions and rowmotion on rectangular and trapezoidal posets, by Joseph Johnson and Ricky Liu (preprint).

• Charmed roots and the Kroweras complement, by Benjamin Dequêne, Gabriel Frieden, Alessandro Iraci, Florian Schreier-Aigner, Hugh Thomas, and Nathan Williams, Journal of the London Mathematical Society (2024) [Interactive Presentation] 

• Toggleability Spaces of Fences, by Alec Mertin and Svetlana Poznanović, Electronic Journal of Combinatorics (2024).

• P-strict promotion and Q-partition rowmotion: the graded case, by Joseph Bernstein, Jessica Striker, and Corey Vorland, European Journal of Combinatorics (2024).

• Toggling, rowmotion, and homomesy on interval-closed sets, by Jennifer Elder, Nadia Lafrenière, Erin McNicholas, Jessica Striker, and Amanda Welch, Journal of Combinatorics (2024). 

• Torsors and tilings from toric toggling, by Colin Defant, Michael Joseph, Matthew Macauley, and Alex McDonough, Algebraic Combinatorics (2024). 

• Rowmotion of m-Tamari and biCambrian lattices, by Colin Defant and James Lin, Combinatorial Theory (2024). 

• Rowmotion Markov chains, by Colin Defant, Rupert Li, and Evita Nestoridi, Advances in Applied Mathematics (2024). 

• Semidistrim lattices, by Colin Defant and Nathan Williams, Forum of Mathematics, Sigma (2023). 

• Rowmotion on fences, by Sergi Elizalde, Mathew Plante, Tom Roby, Bruce Sagan, Algebraic Combinatorics (2023)

• Rowmotion on 321-Avoiding Permutations, by Ben Adenbaum and Sergi Elizalde, Electronic Journal of Combinatorics (2023). 

• The birational Lalanne-Kreweras involution, by Sam Hopkins and Michael Joseph. Algebraic Combinatorics (2022).

• Rowmotion orbits of trapezoid posets, by Quang Vu Dao, Julian Wellman, Calvin Yost-Wolff, and Sylvester W Zhang  Electronic Journal of Combinatorics (2022)

• Minuscule analogues of the plane partition periodicity conjecture of Cameron and Fon-Der-Flaass, by Oliver Pechenik, Combinatorial Theory (2022).

• P-strict promotion and B-bounded rowmotion, with applications to tableaux of many flavors, by Joseph Bernstein, Jessica Striker, and Corey Vorland, Combinatorial Theory (2021). 

• Symmetry of Narayana numbers and rowvacuation of root posets, by Colin Defant and Sam Hopkins, Forum of Mathematics, Sigma (2021). 

• Birational and noncommutative lifts of antichain toggling and rowmotion, by Michael Joseph and Tom Roby, Algebraic Combinatorics (2020)

• Dynamics of plane partitions: Proof of the Cameron–Fon-Der-Flaass conjecture, by Rebecca Patrias and Oliver Pechenik, Forum of Mathematics Sigma (2020).

• Rowmotion and increasing labeling promotion, by Kevin Dilks, Jessica Striker, and Corey Vorland, Journal of Combinatorial Theory Series A (2019).

• Rowmotion in slow motion, by Hugh Thomas and Nathan Williams. Proceedings of the LMS (2019).

• Independence Posets, by Hugh Thomas and Nathan Williams. Journal of Combinatorics (2019) [Interactive Poster] 

• Antichain Toggling and Rowmotion, by Michael Joseph, Electronic Journal of Combinatorics (2019).

• Orbits of plane partitions of exceptional Lie type, by Holly Mandel and Oliver Pechenik, European Journal of Combinatorics (2018).

• Rowmotion and generalized toggle groups, by Jessica Striker, Discrete Math & Theoretical Computer Science (2018).

• Resonance in orbits of plane partitions and increasing tableaux, by Kevin Dilks, Jessica Striker, and Oliver Pechenik, Journal of Combinatorial Theory Series A (2017).

• The toggle group, homomesy, and the Razumov-Stroganov correspondence, by Jessica Striker, Electronic Journal of Combinatorics (2015).

• A uniform bijection between nonnesting and noncrossing partitions, by Drew Armstrong, Christian Stump and Hugh Thomas. Transactions of the AMS (2013).

• Promotion and rowmotion, by Jessica Striker and Nathan Williams, European Journal of Combinatorics (2012).

• On orbits of antichains of positive roots, by Dmitri Panyushev. European Journal of Combinatorics (2009).

• Groups generated by involutions, Gel’fand-Tsetlin patterns, and combinatorics of Young tableaux, by Arkadiy Berenstein and Anatol Kirillov, Algebra i Analiz 7 (1995) = St. Petersburg Math. J., 7 (1996).

• Orbits of antichains revisited, by P.J. Cameron and D.G. Fon-Der-Flaass. European Journal of Combinatorics (1995).

• On the period of an operator, defined on antichains, by Brouwer and Schrijver, Stichting Mathematisch Centrum. Zuivere Wiskunde (1974).

Cyclic Sieving:

• The affine Tamari lattice, by Grant Barkley and Colin Defant, (preprint). 

• Cyclic sieving on permutations -- an analysis of maps and statistics in the FindStat database, by Ashleigh Adams, Jennifer Elder, Nadia Lafrenière, Erin McNicholas, Jessica Striker, and Amanda Welch, (preprint).

• Permutoric promotion: gliding globs, sliding stones, and colliding coins, by Colin Defant, Rachana Madhukara, and Hugh Thomas, Combinatorial Theory (2024). 

• Order polynomial product formulas and poset dynamics, by Sam Hopkins. In Open Problems in Algebraic Combinatorics, Proceedings of Symposia in Pure Mathematics (2024).

• Curious cyclic sieving on increasing tableaux, by Christian Gaetz, Oliver Pechenik, Jessica Striker, and Joshua Swanson, Enumerative Combinatorics and Applications (2022).

• Parity-Unimodality and a Cyclic Sieving Phenomenon for Necklaces, by Eric N. Stucky, SIAM Journal on Discrete Mathematics (2021).

•  Skew characters and cyclic sieving, by Per Alexandersson, Stephan Pfannerer, Martin Rubey, and Joakim Uhlin, Forum of Math Sigma (2021).

• Promotion on oscillating and alternating tableaux and rotation of matchings and permutations,  by Stephan Pfannerer, Martin Rubey, and Bruce Westbury, AlCo (2020).

• Cyclic sieving for plane partitions and symmetry, by Sam Hopkins. SIGMA (2020).

• Sections 6.6 and 7.9 of Combinatorics: The Art of Counting, by Bruce E. Sagan, Graduate Studies in Mathematics, AMS (2020).

• Cyclic sieving and cluster duality of Grassmannian, by Linhui Shen and Daping Weng, SIGMA (2020).

• Orbits of plane partitions of exceptional Lie type, by Holly Mandel and Oliver Pechenik, European Journal of Combinatorics (2018).

• Increasing tableaux, Narayana numbers and an instance of the cyclic sieving phenomenon, by T. Pressey, A. Stokke, and T.I. Visentin, Annals of Combinatorics (2016).

• Cyclic sieving, rotation, and geometric representation theory, by Bruce Fontaine and Joel Kamnitzer, Selecta (2014).

• Jeu-de-taquin promotion and a cyclic sieving phenomenon for semistandard hook tableaux, by M. Bennett, B.W. Madill, and A. Stokke, Discrete Mathematics (2014).

• Cyclic symmetry of the scaled simplex, by Hugh Thomas and Nathan Williams. Journal of Algebraic Combinatorics (2014).

• Promotion and rowmotion, by Jessica Striker and Nathan Williams, European Journal of Combinatorics (2012).

• The cyclic sieving phenomenon: A survey, by Bruce E. Sagan, Surveys in Combinatorics, London Mathematical Society Lecture Note Series, (2011).

• Cyclic sieving of noncrossing partitions for complex reflection groups, by David Bessis and Vic Reiner, Annals of Combinatorics (2011).

• Cyclic sieving, promotion, and representation theory, by Brendon Rhoades. Journal of Combinatorial Theory, Series A (2010).

• The cyclic sieving phenomenon, by Vic Reiner, Dennis Stanton, and Dennis White, Journal of Combinatorial Theory Series A (2004).

• Canonical bases and self-evacuating tableaux, by John Stembridge, Duke (1996).

Homomesy:

• Interval-closed set rowmotion and homomesy on products of two chains, by Nadia Lafrenière, Joel Brewster Lewis, Erin McNicholas, Jessica Striker, and Amanda Welch, (preprint).

• Homomesy on permutations with toggling actions, by William Dowling and Nadia Lafreniere (preprint).

• Homomesies on permutations - an analysis of maps and statistics in the FindStat database, by Jennifer Elder, Nadia Lafrenière, Erin McNicholas, Jessica Striker, and Amanda Welch, Mathematics of Computation (2024).

• Toggling, rowmotion, and homomesy on interval-closed sets, by Jennifer Elder, Nadia Lafrenière, Erin McNicholas, Jessica Striker, and Amanda Welch, Journal of Combinatorics (2024).

• Homomesy via toggleability statistics, by Colin Defant, Sam Hopkins, Svetlana Poznanovic, and James Propp, Combinatorial Theory (2023).

• Minuscule doppelgängers, the coincidental down-degree expectations property, and rowmotion, by Sam Hopkins. Experimental Mathematics (2022).

• The CDE property for skew vexillary permutations, by Sam Hopkins. Journal of Combinatorial Theory, Series A (2019).

• The CDE property for minuscule lattices, by Sam Hopkins. Journal of Combinatorial Theory, Series A (2017).

• The expected jaggedness of order ideals, by Melody Chan, Shahrzad Haddadan, Sam Hopkins, and Luca Moci. Forum of Mathematics, Sigma (2017).

• Proofs and generalizations of a homomesy conjecture of Propp and Roby, by Jonathan Bloom, Oliver Pechenik, and Dan Saracino, Discrete Mathematics (2016).

• The toggle group, homomesy, and the Razumov-Stroganov correspondence, by Jessica Striker, Electronic Journal of Combinatorics (2015).

• Homomesy in products of two chains, by James Propp and Tom Roby, Electronic Journal of Combinatorics (2015).

Resonance:

• Orbits of plane partitions of exceptional Lie type, by Holly Mandel and Oliver Pechenik, European Journal of Combinatorics (2018).

• Resonance in orbits of plane partitions and increasing tableaux, by Kevin Dilks, Jessica Striker, and Oliver Pechenik, Journal of Combinatorial Theory Series A (2017).

• Promotion of increasing tableaux: Frames and homomesies, by Oliver Pechenik, Electronic Journal of Combinatorics (2017).

• A large dihedral symmetry of the set of alternating sign matrices, by Benjamin Wieland, Electronic Journal of Combinatorics (2000).

Combinatorial Billiards:

• Random subwords and billiard walks in affine Weyl groups, by Colin Defant, Pakawut Jiradilok, and Elchanan Mossel, (preprint). 

• Random combinatorial billiards and stoned exclusion processes, by Colin Defant, (preprint). 

• Toric promotion with reflections and refractions, by Ashleigh Adams, Colin Defant, and Jessica Striker, (preprint). 

• The maximum number of cycles in a triangular-grid billiards system with a given perimeter, by Honglin Zhu, (preprint). 

• Homology in combinatorial refraction billiards, by Colin Defant and Derek Liu, Research in the Mathematical Sciences (2025). 

• Bender--Knuth billiards in Coxeter groups, by Grant Barkley, Colin Defant, Eliot Hodges, Noah Kravitz, and Mitchell Lee, Forum of Mathematics, Sigma (2025). 

• Triangular-grid billiards and plabic graphs, by Colin Defant and Pakawut Jiradilok, Combinatorial Theory (2023)

• Toric promotion, by Colin Defant, Proceedings of the American Mathematical Society (2022). 

• Channels, billiards, and perfect matching 2-divisibility, by Grant T. Barkley and Ricky Ini Liu, Electronic Journal of Combinatorics (2021). 

Noninvertible Dynamics:

• Pop-stack operators for torsion classes and Cambrian lattices, by Emily Barnard, Colin Defant, and Eric J. Hanson, (preprint). 

• The pop-stack operator on ornamentation lattices, by Khalid Ajran and Colin Defant, (preprint). 

• Bulgarian solitaire: a new representation for depth generating functions, by A.J. Harris and Son Nguyen, (preprint). 

• Periodic points of consecutive-pattern-avoiding stack-sorting maps, Ilaria Seidel and Nathan Sun, (preprint). 

• Bender--Knuth billiards in Coxeter groups, by Grant Barkley, Colin Defant, Eliot Hodges, Noah Kravitz, and Mitchell Lee, Forum of Mathematics, Sigma (2025). 

• Dynamics of pop-tsack torsing, by Anqi Li, Advances in Applied Mathematics, (2025). 

• Deterministic stack-sorting for set partitions, by Janabel Xia, Enumerative Combinatorics and Applications (2024). 

• On promotion and quasi-tangled labelings of posets, by Eliot Hodges, Annals of Combinatorics (2024). 

• Pop-stack-sorting for Coxeter groups, by Colin Defant, Combinatorial Theory (2022). 

• Stack-sorting for Coxeter groups, by Colin Defant, Combinatorial Theory (2022). 

• Crystal pop-stack sorting and type A crystal lattices, by Colin Defant and Nathan Williams, European Journal of Combinatorics (2022). 

• Promotion sorting, by Colin Defant and Noah Kravitz, Order (2022). 

• Coxeter pop-tsack torsing, by Colin Defant and Nathan Williams, Algebraic Combinatorics (2022). 

• Meeting covered elements in $\nu$-Tamari lattices, by Colin Defant, Advances in Applied Mathematics (2022). 

• The pop-stack-sorting operator on Tamari lattices, by Letong Hong, Advances in Applied Mathematics (2022). 

• Restricted stacks as functions, by Katalin Berlow, Discrete Mathematics (2021). 

• Stack-sorting with consecutive-pattern-avoiding stacks, by Colin Defant and Kai Zheng, Advances in Applied Mathematics (2021). 

• Fertility monotonicity and average complexity of the stack-sorting map, by Colin Defant, European Journal of Combinatorics (2021). 

• Highly sorted permutations and Bell numbers, by Colin Defant, Enumerative Combinatorics and Applications (2021). 

• Quantifying noninvertibility in discrete dynamical systems, by Colin Defant and James Propp, Electronic Journal of Combinatorics (2020). 

• Descents in t-sorted permutations, by Colin Defant, Journal of Combinatorics (2020). 

• Bulgarian Solitaire, by Suzanne Dorée. In Resources for Teaching Discrete Mathematics: Classroom Projects, History Modules, and Articles, edited by Brian Hopkins, Mathematical Association of America (2009).

• Bulgarian solitaire, by Ethan Akin and Morton Davis, The American Mathematical Monthly, (1985). 

Algebraic Applications:

• Rowmotion and Echelonmotion by Colin Defant, Yuhan Jiang, Rene Marczinzik, Adrien Segovia, David E Speyer, Hugh Thomas, Nathan Williams (preprint).

• Rotation-invariant web bases from hourglass plabic graphs, by Christian Gaetz, Oliver Pechenik, Stephan Pfannerer, Jessica Striker, and Joshua P. Swanson (preprint).

• Auslander regular algebras and Coxeter matrices by Viktória Klász, Rene Marczinzik, and Hugh Thomas (preprint).

• Web bases in degree two from hourglass plabic graphs, by Christian Gaetz, Oliver Pechenik, Stephan Pfannerer, Jessica Striker, and Joshua P. Swanson, International Math Research Notices (2025).

• Web invariants for flamingo Specht modules, by Chris Fraser, Rebecca Patrias, Oliver Pechenik, and Jessica Striker, Algebraic Combinatorics (2025).

• On the interaction of the Coxeter transformation and the rowmotion bijection by René Marczinzik, Hugh Thomas, Emine Yıldırım, Journal of Combinatorial Algebra (2024).

• Minuscule reverse plane partitions via quiver representations, by Alexander Garver, Rebecca Patrias, and Hugh Thomas, Selecta (2023).

• A web basis of invariant polynomials from noncrossing partitions, by Rebecca Patrias, Oliver Pechenik, and Jessica Striker, Advances in Mathematics (2022).

• Distributive lattices and Auslander regular algebras, by Osamu Iyama and Rene Marczinzik. Advances in Math (2022).

• A skein action of the symmetric group on noncrossing partitions, by Brendon Rhoades, Journal of Algebraic Combinatorics (2017).