Perron identity for arbitrary broken lines
Oleg Karpenkov, Matty van-Son
TL;DR
This paper generalizes the Perron identity, originally for continued fractions, to arbitrary broken lines using Markov-Davenport forms, expanding the mathematical understanding of binary quadratic forms and their geometric representations.
Contribution
It introduces a generalized Perron identity applicable to arbitrary broken lines, extending previous work limited to ordinary continued fractions.
Findings
Generalization of Perron identity to broken lines
Application to Markov-Davenport forms
Enhanced understanding of binary quadratic forms
Abstract
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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Advanced Topics in Algebra