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Teoreticheskaya i Matematicheskaya Fizika, 2006, Volume 149, Number 3, Pages 395–408
DOI: https://doi.org/10.4213/tmf5531 (Mi tmf5531) 		 
This article is cited in 16 scientific papers (total in 16 papers)

Enumeration of quarter-turn-symmetric alternating-sign matrices of odd order

A. V. Razumov, Yu. G. Stroganov

Institute for High Energy Physics
Full-text PDF (504 kB) Citations (16)
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DOI: https://doi.org/10.4213/tmf5531
Abstract: Kuperberg showed that the partition function of the square-ice model related to quarter-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 bijection with the quarter-turn-symmetric alternating-sign matrices of odd order and show that the partition function of this model can be written similarly. In particular, this allows proving Robbins's conjectures related to the enumeration of quarter-turn-symmetric alternating-sign matrices.
Keywords: alternating-sign matrix, enumeration, square-ice model.
Received: 04.05.2006
English version:
Theoretical and Mathematical Physics, 2006, Volume 149, Issue 3, Pages 1639–1650
DOI: https://doi.org/10.1007/s11232-006-0148-8
Bibliographic databases:
Language: Russian
Citation: A. V. Razumov, Yu. G. Stroganov, “Enumeration of quarter-turn-symmetric alternating-sign matrices of odd order”, TMF, 149:3 (2006), 395–408; Theoret. and Math. Phys., 149:3 (2006), 1639–1650
Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf5531
  • https://www.mathnet.ru/eng/tmf/v149/i3/p395
    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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