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Social sciences
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The polynomial method in Galois geometry refers to a method of obtaining geometrical information on a geometric structure by studying the algebraic properties of a polynomial associated to the geometric structure. However, this method has its restrictions, of which one very particular restriction is due to the fact that the polynomial is defined over a finite field, which has a non-zero characteristic. We present a new approach by associating a polynomial over the field of p-adic numbers to a geometric structure, which avoids the problem of the non-zero characteristic, and which can lead to stronger results. The proposed research is to be carried out in cooperation with prof. dr. Tam´as Sz˝onyi (E¨otv¨os Lor´and University, Budapest) and prof. dr. Simeon Ball (Universitat Polit`ecnica de Catalunya, Barcelona).