Zobrazeno 1 - 10
of 17
pro vyhledávání: '"Van Son, Matty"'
We use a class of Farey graphs introduced by the final three authors to enumerate the tame friezes over $\mathbb{Z}/n\mathbb{Z}$. Using the same strategy we enumerate the tame regular friezes over $\mathbb{Z}/n\mathbb{Z}$, thereby reproving a recent
Externí odkaz:
http://arxiv.org/abs/2410.23400
Autor:
Karpenkov, Oleg, van Son, Matty
In this paper we develop a new geometric approach to subtractive continued fraction algorithms in high dimensions. We adapt a version of Farey summation to the geometric techniques proposed by F. Klein in 1895. More specifically we introduce Farey po
Externí odkaz:
http://arxiv.org/abs/2410.13091
Frieze patterns have attracted significant attention recently, motivated by their relationship with cluster algebras. A longstanding open problem has been to provide a combinatorial model for frieze patterns over the ring of integers modulo $n$ akin
Externí odkaz:
http://arxiv.org/abs/2312.12953
Autor:
van Son, Matty
In this note we study the integer solutions of Cayley's cubic equation. We find infinite families of solutions built from recurrence relations. We use these solutions to solve certain general Pell equations. We also show the similarities and differen
Externí odkaz:
http://arxiv.org/abs/2108.02441
Autor:
van Son, Matty
We study an extension to the uniqueness conjecture for Markov numbers. For any three positive integers $m\geq a$ and $m\geq b$ satisfying $a^2+b^2+m^2=3abm$, this conjecture states that the triple $(a,m,b)$ is uniquely determined by the Markov number
Externí odkaz:
http://arxiv.org/abs/1911.00746
Autor:
Karpenkov, Oleg, van-Son, Matty
In this paper we introduce generalised Markov numbers and extend the classical Markov theory for the discrete Markov spectrum to the case of generalised Markov numbers. In particular we show recursive properties for these numbers and find correspondi
Externí odkaz:
http://arxiv.org/abs/1809.01688
Autor:
van-Son, Matty
We study the periods of Markov sequences, which are derived from the continued fraction expression of elements in the Markov spectrum. This spectrum is the set of minimal values of indefinite binary quadratic forms that are specially normalised. We s
Externí odkaz:
http://arxiv.org/abs/1804.10802
Autor:
Karpenkov, Oleg, van-Son, Matty
In this paper we study the values of Markov-Davenport forms, which are specially normalized binary quadratic forms. We generalize the Perron identity for ordinary continued fractions for sails to the case of arbitrary broken lines.
Externí odkaz:
http://arxiv.org/abs/1708.07396
Autor:
Karpenkov, Oleg, van Son, Matty
Publikováno v:
In Journal of Number Theory August 2020 213:16-66
Autor:
KARPENKOV, Oleg, VAN-SON, Matty
Publikováno v:
Journal de Théorie des Nombres de Bordeaux, 2019 Jan 01. 31(1), 131-144.
Externí odkaz:
https://www.jstor.org/stable/26730889