Generating Integrally Indecomposable Newton Polygons with Arbitrary Many Vertices

Petar Ðapić, Ivan Pavkov, Siniša Crvenković and Ilija Tanackov
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Petar Ðapić: Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovića 3, 21000 Novi Sad, Serbia
Ivan Pavkov: Faculty of Mathematics and Computer Science, Alfa BK University, Palmira Toljatija 3, 11000 Belgrade, Serbia
Siniša Crvenković: Faculty of Mathematics and Computer Science, Alfa BK University, Palmira Toljatija 3, 11000 Belgrade, Serbia
Ilija Tanackov: Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, Serbia

Mathematics, 2022, vol. 10, issue 14, 1-10

Abstract: In this paper we shall give another proof of a special case of Gao’s theorem for generating integrally indecomposable polygons in the sense of Minkowski. The approach of proving this theorem will enable us to give an effective algorithm for construction integrally indecomposable convex integral polygons with arbitrary many vertices. In such a way, classes of absolute irreducible bivariate polynomials corresponding to those indecomposable Newton polygons are generated.

Keywords: Newton polygon; Minkowski sum; irreducible polynomial; geometrical approach (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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