Geodesic
Consistency on Cubic Lattices for Determinants of Arbitrary Orders
Informatics and Automation, Geometry, topology, and mathematical physics. II, Tome 266 (2009), pp. 202-217.

Voir la notice de l'article provenant de la source Math-Net.Ru

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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     author = {O. I. Mokhov},
     title = {Consistency on {Cubic} {Lattices} for {Determinants} of {Arbitrary} {Orders}},
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O. I. Mokhov. Consistency on Cubic Lattices for Determinants of Arbitrary Orders. Informatics and Automation, Geometry, topology, and mathematical physics. II, Tome 266 (2009), pp. 202-217. http://geodesic.mathdoc.fr/item/TRSPY_2009_266_a10/

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