The Many Faces of Alternating-Sign MatricesArticle
Authors: James Propp 1
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James Propp
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.
Andrew Beveridge;Ian Calaway;Kristin Heysse, 2021, De Finetti Lattices and Magog Triangles, The Electronic Journal of Combinatorics, 28, 1, 10.37236/9246, https://doi.org/10.37236/9246.
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.
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.
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.
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.
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, arXiv (Cornell University), 319, 1-3, pp. 83-101, 10.1016/j.tcs.2004.02.020, http://arxiv.org/abs/math/0302344.