Polynomials in Finite Geometry

The main topic is what the title indicates: to collect, survey and categorize the results and theories achieved in the last 30 years with "polynomial methods," mostly (but not exclusively) in finite geometries. It contains techniques based on the careful examination of coefficients of polynomials, resultants, algebraic curves, subspaces generated by certain polynomials, random-like behaviour, etc. Our polynomials are usually defined over a finite field, and they express some combinatorial or geometric property of a combinatorial or geometric structure. We go through several types of applications of the methods. There are more than a hundred exercises with short solutions.

Subiectul principal este ceea ce indica titlul: sa colectam, sa analizam si sa clasificam rezultatele si teoriile obtinute in ultimii 30 de ani cu „metode polinomiale”, mai ales (dar nu exclusiv) in geometrii finite. Contine tehnici bazate pe examinarea atenta a coeficientilor polinoamelor, rezultantilor, curbelor algebrice, subespaiilor generate de anumite polinoame, comportament aleatoriu etc.