11 citations · 22 across the 7 of their papers we have counts for
9 papers
The Birth of Number Theory (Book VII of Euclid's Elements) from the Arithmetization of Pythagorean Music
Stelios Negrepontis, Vassiliki Farmaki, Angeliki Pisimisi
Book VII of Euclid's Elements represents a remarkable mathematical achievement, marking the birth of number theory. Although it falls short of explicitly stating the Fundamental Th…
The anthyphairetic reconstruction of the original Pythagorean proof of incommensurability, by means of the restoration of Book II of the Elements to its original Pythagorean form
Stelios Negrepontis, Vassiliki Farmaki
Unquestionably the greatest discovery of the Pythagoreans is the existence of incommensurable magnitudes, most probably the incommensurability of the diameter to the side of a squa…
Topological Dynamics indexed by words
Vassiliki Farmaki, Andreas Koutsogiannis
Starting with a combinatorial partition theorem for words over an infinite alphabet dominated by a fixed sequence, established recently by the authors, we prove recurrence results…
Ramsey Theory for Words Representing Rationals
Vassiliki Farmaki, Andreas Koutsogiannis
Ramsey theory for words over a finite alphabet was unified in the work of Carlson and Furstenberg-Katznelson. Carlson, in the same work, outlined a method to extend the theory for…
Ramsey Theory for Words over an Infinite Alphabet
Vassiliki Farmaki
A complete partition theory is presented for omega-located words (and omega-words), namely for located words over an infinite alphabet dominated by a fixed increasing sequence. Thi…
Schreier Sets in Ramsey Theory
V. Farmaki, S. Negrepontis
We show that Ramsey theory, a domain presently conceived to guarantee the existence of large homogeneous sets for partitions on k-tuples of words (for every natural number k) over…