Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Author:
Καραγεώργος Δημήτριος
Supervisors info:
Βασιλική Φαρμάκη Καθηγήτρια ΕΚΠΑ, Αριστείδης Κατάβολος Καθηγητής ΕΚΠΑ, Νίκόλαος Παπαναστασίου Αναπλ. Καθηγητής ΕΚΠΑ
Original Title:
Πολυωνυμικές επεκτάσεις του Θεωρήματος van der Waerden
Summary:
The theme of this Master Thesis is the fundamental combinatorial theorem of van
der Waerden. We present equivalent forms of this theorem as well as
improvements and
extensions, as the polynomial van der Waerden Theorem proved by Bergelson and
Leibman
(1996).
We include a proof of the topological form of van der Waerden's Theorem in its
multidimensional form given by Furstenberg and Weiss with the help of the
theory of topological dynamical systems and the equivalent Gallai's Theorem.
Also we give the analogous proof of the topological equivalent form of the
polynomial van der Waerden Theorem given by Bergelson and Leibman.
Keywords:
van der Waerden, Gallai, Topological Dynamical Systems, Furstenberg-Weiss Theorem, Polynomial van der Waerden's Theorem
