Homomesy in products of two chains

James Propp; Tom Roby

doi:10.46298/dmtcs.2356

James Propp ; Tom Roby - Homomesy in products of two chains

dmtcs:2356 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.2356

Homomesy in products of two chainsConference paper

Authors: James Propp ¹; Tom Roby ²

1 Department of Mathematics [Lowell]
2 University of Connecticut

Many cyclic actions $τ$ on a finite set $\mathcal{S}$ ; of combinatorial objects, along with a natural statistic $f$ on $\mathcal{S}$, exhibit ``homomesy'': the average of $f$ over each $τ$-orbit in $\mathcal{S} $ is the same as the average of $f$ over the whole set $\mathcal{S} $. This phenomenon was first noticed by Panyushev in 2007 in the context of antichains in root posets; Armstrong, Stump, and Thomas proved Panyushev's conjecture in 2011. We describe a theoretical framework for results of this kind and discuss old and new results for the actions of promotion and rowmotion on the poset that is the product of two chains.

https://doi.org/10.46298/dmtcs.2356

Source: HAL:hal-01229696v1

Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)

Section: Proceedings

Published on: January 1, 2013

Imported on: November 21, 2016

Keywords: [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [en] antichains, combinatorial ergodicity, homomesy, orbit, order ideals, poset, product of chains, promotion, rowmotion, sandpile, toggle group.

Funding:

Source : OpenAIRE Graph

Deterministic analogues of random processes; Funder: National Science Foundation; Code: 1001905

Bibliographic References

21 Documents citing this article

Sam Hopkins, 2024, Order polynomial product formulas and poset dynamics, Proceedings of symposia in pure mathematics, pp. 135-157, 10.1090/pspum/110/02006.

Jennifer Elder;Nadia Lafrenière;Erin McNicholas;Jessica Striker;Amanda Welch, 2023, Homomesies on permutations: An analysis of maps and statistics in the FindStat database, Mathematics of Computation, 93, 346, pp. 921-976, 10.1090/mcom/3866.

Joseph Bernstein;Jessica Striker;Corey Vorland, 2023, P-strict promotion and Q-partition rowmotion: The graded case, European Journal of Combinatorics, 115, pp. 103776, 10.1016/j.ejc.2023.103776.

Anders Skovsted Buch;Chengxi Wang, 2021, Positivity determines the quantum cohomology of Grassmannians, Algebra & Number Theory, 15, 6, pp. 1505-1521, 10.2140/ant.2021.15.1505.

Colin Defant;Sam Hopkins, 2021, Symmetry of Narayana Numbers and Rowvacuation of Root Posets, Forum of Mathematics Sigma, 9, 10.1017/fms.2021.47, https://doi.org/10.1017/fms.2021.47.

David Einstein;James Propp, 2021, Combinatorial, piecewise-linear, and birational homomesy for products of two chains, Algebraic Combinatorics, 4, 2, pp. 201-224, 10.5802/alco.139, https://doi.org/10.5802/alco.139.

Kevin Dilks;Oliver Pechenik;Jessica Striker, 2020, Resonance in orbits of plane partitions, Discrete Mathematics & Theoretical Computer Science, DMTCS Proceedings, 28th..., 10.46298/dmtcs.6394, https://doi.org/10.46298/dmtcs.6394.

Michael Joseph;Tom Roby, 2020, Birational and noncommutative lifts of antichain toggling and rowmotion, Algebraic Combinatorics, 3, 4, pp. 955-984, 10.5802/alco.125, https://doi.org/10.5802/alco.125.

Rebecca Patrias;Oliver Pechenik, 2020, Dynamics of plane partitions: Proof of the Cameron–Fon-Der-Flaass conjecture, Forum of Mathematics Sigma, 8, 10.1017/fms.2020.61, https://doi.org/10.1017/fms.2020.61.

Sam Hopkins;Sam Hopkins, 2020, Minuscule Doppelgängers, The Coincidental down-Degree Expectations Property, and Rowmotion, arXiv (Cornell University), 31, 3, pp. 946-974, 10.1080/10586458.2020.1731881, http://arxiv.org/abs/1902.07301.

H. Thomas;N. Williams;H. Thomas;N. Williams, 2019, Rowmotion in slow motion, arXiv (Cornell University), 119, 5, pp. 1149-1178, 10.1112/plms.12251, http://arxiv.org/abs/1712.10123.

Sam Hopkins, 2019, The CDE property for skew vexillary permutations, Journal of Combinatorial Theory Series A, 168, pp. 164-218, 10.1016/j.jcta.2019.06.005, https://doi.org/10.1016/j.jcta.2019.06.005.

Holly Mandel;Oliver Pechenik, 2018, Orbits of plane partitions of exceptional Lie type, arXiv (Cornell University), 74, pp. 90-109, 10.1016/j.ejc.2018.07.007, http://arxiv.org/abs/1712.09180.

Kevin Dilks;Jessica Striker;Corey Vorland, 2018, Rowmotion and increasing labeling promotion, arXiv (Cornell University), 164, pp. 72-108, 10.1016/j.jcta.2018.12.007, http://arxiv.org/abs/1710.07179.

Kevin Dilks;Oliver Pechenik;Jessica Striker, 2017, Resonance in orbits of plane partitions and increasing tableaux, arXiv (Cornell University), 148, pp. 244-274, 10.1016/j.jcta.2016.12.007, http://arxiv.org/abs/1512.00365.

MELODY CHAN;SHAHRZAD HADDADAN;SAM HOPKINS;LUCA MOCI, 2017, THE EXPECTED JAGGEDNESS OF ORDER IDEALS, Forum of Mathematics Sigma, 5, 10.1017/fms.2017.5, https://doi.org/10.1017/fms.2017.5.

Sam Hopkins, 2017, The CDE property for minuscule lattices, arXiv (Cornell University), 152, pp. 45-103, 10.1016/j.jcta.2017.06.006, http://arxiv.org/abs/1606.06248.

Anne Schilling;Nicolas M. Thiéry;Graham White;Nathan Williams, 2016, Braid moves in commutation classes of the symmetric group, European Journal of Combinatorics, 62, pp. 15-34, 10.1016/j.ejc.2016.10.008, https://doi.org/10.1016/j.ejc.2016.10.008.

Tom Roby, 2016, Dynamical algebraic combinatorics and the homomesy phenomenon, The IMA volumes in mathematics and its applications, pp. 619-652, 10.1007/978-3-319-24298-9_25.

Jessica Striker, 2015, The Toggle Group, Homomesy, and the Razumov-Stroganov Correspondence, The Electronic Journal of Combinatorics, 22, 2, 10.37236/5158, https://doi.org/10.37236/5158.

Jonathan Bloom;Oliver Pechenik;Dan Saracino, 2015, Proofs and generalizations of a homomesy conjecture of Propp and Roby, arXiv (Cornell University), 339, 1, pp. 194-206, 10.1016/j.disc.2015.08.011, http://arxiv.org/abs/1308.0546.

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