The Many Faces of Alternating-Sign Matrices

James Propp

doi:10.46298/dmtcs.2292

James Propp - The Many Faces of Alternating-Sign Matrices

dmtcs:2292 - Discrete Mathematics & Theoretical Computer Science, January 1, 2001, DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001) - https://doi.org/10.46298/dmtcs.2292

The Many Faces of Alternating-Sign MatricesConference paper

Authors: James Propp ¹

1 Department of Mathematics [Madison]

I give a survey of different combinatorial forms of alternating-sign matrices, starting with the original form introduced by Mills, Robbins and Rumsey as well as corner-sum matrices, height-function matrices, three-colorings, monotone triangles, tetrahedral order ideals, square ice, gasket-and-basket tilings and full packings of loops.

https://doi.org/10.46298/dmtcs.2292

Source: HAL:hal-01182972v1

Volume: DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001)

Section: Proceedings

Published on: January 1, 2001

Imported on: November 21, 2016

Keywords: [INFO]Computer Science [cs], [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], [en] Alternating-Sign Matrices, Tilings

Funding:

Source : OpenAIRE Graph

RootDetect: Remote Detection and Precision Management of Root Health; Code: 53706

Bibliographic References

24 Documents citing this article

Arvind Ayyer;Sunil Chhita;Kurt Johansson, 2023, GOE fluctuations for the maximum of the top path in alternating sign matrices, Duke Mathematical Journal, 172, 10, 10.1215/00127094-2022-0075.

Pavel Galashin, 2021, Periodicity and integrability for the cube recurrence, arXiv (Cornell University), 299, 3-4, pp. 1533-1563, 10.1007/s00209-020-02667-6, http://arxiv.org/abs/1704.05570.

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.

Linnea Hietala, 2020, A Combinatorial Description of Certain Polynomials Related to the XYZ Spin Chain, Symmetry Integrability and Geometry Methods and Applications, 10.3842/sigma.2020.101, https://doi.org/10.3842/sigma.2020.101.

Masato Kobayashi, 2019, Weighted Counting of Inversions on Alternating Sign Matrices, Order, 37, 3, pp. 461-477, 10.1007/s11083-019-09515-1.

Ilse Fischer, 2018, Enumeration of alternating sign triangles using a constant term approach, Transactions of the American Mathematical Society, 372, 2, pp. 1485-1508, 10.1090/tran/7652, https://doi.org/10.1090/tran/7652.

Dylan Heuer;Chelsey Morrow;Ben Noteboom;Sara Solhjem;Jessica Striker;et al., 2017, Chained permutations and alternating sign matrices—Inspired by three-person chess, arXiv (Cornell University), 340, 12, pp. 2732-2752, 10.1016/j.disc.2017.08.005, http://arxiv.org/abs/1611.03387.

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.

Dan Romik, 2014, Connectivity Patterns in Loop Percolation I: the Rationality Phenomenon and Constant Term Identities, arXiv (Cornell University), 330, 2, pp. 499-538, 10.1007/s00220-014-2001-5, http://arxiv.org/abs/1303.6341.

Roger E. Behrend, 2013, Multiply-refined enumeration of alternating sign matrices, arXiv (Cornell University), 245, pp. 439-499, 10.1016/j.aim.2013.05.026, http://arxiv.org/abs/1203.3187.

Jessica Striker;Nathan Williams, 2012, Promotion and rowmotion, European Journal of Combinatorics, 33, 8, pp. 1919-1942, 10.1016/j.ejc.2012.05.003.

Richard A. Brualdi;Kathleen P. Kiernan;Seth A. Meyer;Michael W. Schroeder, 2012, Patterns of alternating sign matrices, Linear Algebra and its Applications, 438, 10, pp. 3967-3990, 10.1016/j.laa.2012.03.009.

Paul Zinn-Justin, 2010, A Conjectured Formula for Fully Packed Loop Configurations in a Triangle, The Electronic Journal of Combinatorics, 17, 1, 10.37236/379, https://doi.org/10.37236/379.

Philippe Nadeau, 2010, Fully Packed Loop configurations in a triangle and Littlewood Richardson coefficients, Discrete Mathematics & Theoretical Computer Science, DMTCS Proceedings vol. AN,..., Proceedings, 10.46298/dmtcs.2881, https://doi.org/10.46298/dmtcs.2881.

Hjalmar Rosengren, 2009, An Izergin–Korepin-type identity for the 8VSOS model, with applications to alternating sign matrices, arXiv (Cornell University), 43, 2, pp. 137-155, 10.1016/j.aam.2009.01.003, http://arxiv.org/abs/0801.1229.

Ilse Fischer;Dan Romik, 2009, More refined enumerations of alternating sign matrices, Advances in Mathematics, 222, 6, pp. 2004-2035, 10.1016/j.aim.2009.07.003.

Philippe Duchon, 2008, On the link pattern distribution of quarter-turn symmetric FPL configurations, Discrete Mathematics & Theoretical Computer Science, DMTCS Proceedings vol. AJ,..., Proceedings, 10.46298/dmtcs.3644, https://doi.org/10.46298/dmtcs.3644.

Simone Severini;Simone Severini, 2008, Nondiscriminatory propagation on trees, arXiv (Cornell University), 41, 48, pp. 482002, 10.1088/1751-8113/41/48/482002, http://arxiv.org/abs/0805.0181.

Andrew N.W. Hone, 2007, Laurent Polynomials and Superintegrable Maps, Symmetry Integrability and Geometry Methods and Applications, 10.3842/sigma.2007.022, https://doi.org/10.3842/sigma.2007.022.

André Henriques, 2007, A periodicity theorem for the octahedron recurrence, Journal of Algebraic Combinatorics, 26, 1, pp. 1-26, 10.1007/s10801-006-0045-0.

A. M. Hamel;R. C. King, 2005, U-Turn Alternating Sign Matrices, Symplectic Shifted Tableaux and their Weighted Enumeration, Journal of Algebraic Combinatorics, 21, 4, pp. 395-421, 10.1007/s10801-005-3019-8, https://doi.org/10.1007/s10801-005-3019-8.

David P. Robbins, 2005, A conjecture about Dodgson condensation, Advances in Applied Mathematics, 34, 4, pp. 654-658, 10.1016/j.aam.2004.07.007.

Michael Korn;Igor Pak, 2004, Tilings of rectangles with T-tetrominoes, Theoretical Computer Science, 319, 1-3, pp. 3-27, 10.1016/j.tcs.2004.02.023.

Sébastien Desreux;Martin Matamala;Ivan Rapaport;Eric Rémila, 2004, Domino tilings and related models: space of configurations of domains with holes, Theoretical Computer Science, 319, 1-3, pp. 83-101, 10.1016/j.tcs.2004.02.020.

Sources : OpenCitations, OpenAlex & Crossref

Share and export

Consultation statistics

This page has been seen 593 times.

This article's PDF has been downloaded 649 times.