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 Tr. Mat. Inst. Steklova, 2009, Volume 266, Pages 202–217 (Mi tm1879)

Consistency on Cubic Lattices for Determinants of Arbitrary Orders

O. I. Mokhovab

a Department of Geometry and Topology, Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia
b Centre for Nonlinear Studies, L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Moscow, Russia

Abstract: We consider a special class of two-dimensional discrete equations defined by relations on elementary $N\times N$ squares, $N>2$, of the square lattice $\mathbb Z^2$, and propose a new type of consistency conditions on cubic lattices for such discrete equations that is connected to bending elementary $N\times N$ squares, $N>2$, in the cubic lattice $\mathbb Z^3$. For an arbitrary $N$ we prove such consistency on cubic lattices for two-dimensional discrete equations defined by the condition that the determinants of values of the field at the points of the square lattice $\mathbb Z^2$ that are contained in elementary $N\times N$ squares vanish.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2009, 266, 195–209

Bibliographic databases:

UDC: 512.643.2+511.9+514.74+514.174.6+517.957

Citation: O. I. Mokhov, “Consistency on Cubic Lattices for Determinants of Arbitrary Orders”, Geometry, topology, and mathematical physics. II, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday, Tr. Mat. Inst. Steklova, 266, MAIK Nauka/Interperiodica, Moscow, 2009, 202–217; Proc. Steklov Inst. Math., 266 (2009), 195–209

Citation in format AMSBIB
\Bibitem{Mok09} \by O.~I.~Mokhov \paper Consistency on Cubic Lattices for Determinants of Arbitrary Orders \inbook Geometry, topology, and mathematical physics.~II \bookinfo Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday \serial Tr. Mat. Inst. Steklova \yr 2009 \vol 266 \pages 202--217 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm1879} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2603268} \zmath{https://zbmath.org/?q=an:1259.39005} \elib{http://elibrary.ru/item.asp?id=12901685} \transl \jour Proc. Steklov Inst. Math. \yr 2009 \vol 266 \pages 195--209 \crossref{https://doi.org/10.1134/S0081543809030110} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000270722100011} \elib{http://elibrary.ru/item.asp?id=15305743} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70350373836} 

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

This publication is cited in the following articles:
1. Oleg I. Mokhov, “On Initial Data in the Problem of Consistency on Cubic Lattices for $3\times3$ Determinants”, SIGMA, 7 (2011), 075, 19 pp.
2. Demskoi D.K., Tran D.T., “Darboux integrability of determinant and equations for principal minors”, Nonlinearity, 29:7 (2016), 1973–1991
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