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

Teoreticheskaya i Matematicheskaya Fizika

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor
	Guidelines for authors
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

TMF:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

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)

References:

PDF

HTML

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

\Bibitem{RazStr06}

\by A.~V.~Razumov, Yu.~G.~Stroganov

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

\jour TMF

\yr 2006

\vol 149

\issue 3

\pages 395--408

\mathnet{http://mi.mathnet.ru/tmf5531}

\crossref{https://doi.org/10.4213/tmf5531}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2321099}

\zmath{https://zbmath.org/?q=an:1177.15035}

\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2006TMP...149.1639R}

\elib{https://elibrary.ru/item.asp?id=9433542}

\transl

\jour Theoret. and Math. Phys.

\yr 2006

\vol 149

\issue 3

\pages 1639--1650

\crossref{https://doi.org/10.1007/s11232-006-0148-8}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000243703500007}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33845805764}

Linking options:

https://www.mathnet.ru/eng/tmf5531

https://doi.org/10.4213/tmf5531

https://www.mathnet.ru/eng/tmf/v149/i3/p395

This publication is cited in the following 16 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
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
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
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
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

Statistics & downloads:
Abstract page:	420
Full-text PDF :	213
References:	75
First page:	1

Что такое QR-код?

Registration to the website

Logotypes