A. V. Razumov, Yu. G. Stroganov, “Enumerations of half-turn-symmetric alternating-sign matrices of odd order”, TMF, 148:3 (2006), 357–386; Theoret. and Math. Phys., 148:3 (2006), 1174

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Teoreticheskaya i Matematicheskaya Fizika, 2006, Volume 148, Number 3, Pages 357–386
DOI: https://doi.org/10.4213/tmf2322 (Mi tmf2322)

This article is cited in 21 scientific papers (total in 21 papers)

Enumerations of half-turn-symmetric alternating-sign matrices of odd order

A. V. Razumov, Yu. G. Stroganov

Institute for High Energy Physics

Full-text PDF (697 kB) Citations (21)

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DOI: https://doi.org/10.4213/tmf2322

Abstract: Kuperberg showed that the partition function of the square-ice model related to half-turn-symmetric alternating-sign matrices of even order is the product of two similar factors. We propose a square-ice model whose states are in bijective correspondence with half-turn-symmetric alternating-sign matrices of odd order. The partition function of this model is expressed via the above factors. We find the contributions to the partition function that correspond to the alternating-sign matrices having $1$ or $-1$ as the central entry and establish the related enumerations.

Keywords: alternating-sign matrices, enumerations, square-ice model.

Received: 13.02.2006

English version:
Theoretical and Mathematical Physics, 2006, Volume 148, Issue 3, Pages 1174–1198
DOI: https://doi.org/10.1007/s11232-006-0111-8

Bibliographic databases:

Language: Russian

Citation: A. V. Razumov, Yu. G. Stroganov, “Enumerations of half-turn-symmetric alternating-sign matrices of odd order”, TMF, 148:3 (2006), 357–386; Theoret. and Math. Phys., 148:3 (2006), 1174–1198

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This publication is cited in the following 21 articles:

Fischer I. Saikia M.P., “Refined Enumeration of Symmetry Classes of Alternating Sign Matrices”, J. Comb. Theory Ser. A, 178 (2021), 105350
Bogdan Grechuk, Landscape of 21st Century Mathematics, 2021, 51
Ayyer A. Behrend R.E. Fischer I., “Extreme Diagonally and Antidiagonally Symmetric Alternating Sign Matrices of Odd Order”, Adv. Math., 367 (2020), 107125
Ayyer A., Behrend R.E., “Factorization Theorems For Classical Group Characters, With Applications to Alternating Sign Matrices and Plane Partitions”, J. Comb. Theory Ser. A, 165 (2019), 78–105
Khazret S. Nirov, Alexander V. Razumov, “Vertex Models and Spin Chains in Formulas and Pictures”, SIGMA, 15 (2019), 068, 67 pp.
J. Math. Sci. (N. Y.), 242:5 (2019), 742–752
Behrend R.E. Fischer I. Konvalinka M., “Diagonally and Antidiagonally Symmetric Alternating Sign Matrices of Odd Order”, Adv. Math., 315 (2017), 324–365
Fischer I., “Short proof of the ASM theorem avoiding the six-vertex model”, J. Comb. Theory Ser. A, 144:SI (2016), 139–156
Hamel A.M., King R.C., “Half-Turn Symmetric Alternating Sign Matrices and Tokuyama Type Factorisation For Orthogonal Group Characters”, J. Comb. Theory Ser. A, 131 (2015), 1–31
Brubaker B., Schultz A., “the Six-Vertex Model and Deformations of the Weyl Character Formula”, J. Algebr. Comb., 42:4 (2015), 917–958
Angèle M. Hamel, Ronald C. King, “Half-turn symmetric alternating sign matrices and Tokuyama type factorisation for orthogonal group characters”, Journal of Combinatorial Theory, Series A, 131 (2015), 1
Cantini L. Sportiello A., “A One-Parameter Refinement of the Razumov-Stroganov Correspondence”, J. Comb. Theory Ser. A, 127 (2014), 400–440
Behrend R.E., Di Francesco Ph., Zinn-Justin P., “A Doubly-Refined Enumeration of Alternating Sign Matrices and Descending Plane Partitions”, J. Comb. Theory Ser. A, 120:2 (2013), 409–432
Behrend R.E., “Multiply-Refined Enumeration of Alternating Sign Matrices”, Adv. Math., 245 (2013), 439–499
Paul Zinn-Justin, Springer Proceedings in Mathematics & Statistics, 40, Symmetries, Integrable Systems and Representations, 2013, 599
Behrend R.E., Di Francesco Ph., Zinn-Justin P., “On the weighted enumeration of alternating sign matrices and descending plane partitions”, J Combin Theory Ser A, 119:2 (2012), 331–363
Aval J.-Christophe, Duchon Ph., “Enumeration of alternating sign matrices of even size (quasi-)invariant under a quarter-turn rotation”, Electronic Journal of Combinatorics, 17:1 (2010), R51
A. V. Razumov, Yu. G. Stroganov, “Three-coloring statistical model with domain wall boundary conditions: Trigonometric limit”, Theoret. and Math. Phys., 161:2 (2009), 1451–1459
J.-Ch. Aval, “The symmetry of the partition function of some square ice models”, Theoret. and Math. Phys., 161:3 (2009), 1582–1589
R. Douglas Chatham, “Reflections on the N + k Queens Problem”, The College Mathematics Journal, 40:3 (2009), 204

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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