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3 results on '"Solymosi, Jozsef"'

1. On the Thue–Vinogradov Lemma.

Author

Solymosi, Jozsef

Abstract

We prove an extension of the Thue–Vinogradov lemma. This paper is another example for the application of the polynomial method, Rédei polynomials, and Stepanov's technique. [ABSTRACT FROM AUTHOR]

Published
2021
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2. Incidences and the spectra of graphs.

Author

Solymosi, Jozsef

Abstract

In this contribution we give incidence bounds for arrangements of curves in F q2. As an application, we prove a new result that, if (x, f (x)) is a Sidon set, then either A+A or f(A)+f(A) should be large. The main goal of the paper is to illustrate the use of graph spectral techniques in additive combinatorics. This is an extended version of the talks I gave in the Additive Combinatorics DocCourse held at the CRM in Barcelona and at the conference ˵Fete of Combinatorics″ held in Keszthely. [ABSTRACT FROM AUTHOR]

Published
2009
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3. On a Question of Erdős and Ulam.

Author

Solymosi, Jozsef and de Zeeuw, Frank

Subjects
*DISCRETE geometry, *RATIONAL points (Geometry), *ARITHMETICAL algebraic geometry, *COMBINATORIAL geometry, *COMBINATORICS
Abstract

Ulam asked in 1945 if there is an everywhere dense rational set, i.e., 1 a point set in the plane with all its pairwise distances rational. Erdős conjectured that if a set S has a dense rational subset, then S should be very special. The only known types of examples of sets with dense (or even just infinite) rational subsets are lines and circles. In this paper we prove Erdős’ conjecture for algebraic curves by showing that no irreducible algebraic curve other than a line or a circle contains an infinite rational set. [ABSTRACT FROM AUTHOR]

Published
2010
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