# American Institute of Mathematical Sciences

September  2014, 6(3): 319-333. doi: 10.3934/jgm.2014.6.319

## Discriminantly separable polynomials and quad-equations

 1 The Department of Mathematical Sciences, University of Texas at Dallas, 800 West Campbell Road, Richardson TX 75080, United States 2 Faculty for Traffic and Transport Engineering, University of Belgrade, Vojvode Stepe 305, 11000 Belgrade, Serbia

Received  April 2013 Revised  July 2014 Published  September 2014

We classify the discriminantly separable polynomials of degree two in each of three variables, defined by a property that all the discriminants as polynomials of two variables are factorized as products of two polynomials of one variable each. Our classification is based on the study of structures of zeros of a polynomial component $P$ of a discriminant. This classification is related to the classification of pencils of conics in a delicate way. We establish a relationship between our classification and the classification of integrable quad-equations which has been suggested recently by Adler, Bobenko, and Suris.
Citation: Vladimir Dragović, Katarina Kukić. Discriminantly separable polynomials and quad-equations. Journal of Geometric Mechanics, 2014, 6 (3) : 319-333. doi: 10.3934/jgm.2014.6.319
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