4 citations · 19 across the 20 of their papers we have counts for
22 papers
The Natural Extension for the Triangle Map (a Multi-dimensional Continued Fraction) with An Internal Symmetry from Young Conjugation
Joe Fox, Thomas Garrity
The natural extension of the triangle map (a type of multi-dimensional continued fraction algorithm) is completely described in all possible dimensions. The motivation and inspirat…
Generating New Partition Identities via a Generalized Continued Fraction Algorithm
Wael Baalbaki, Thomas Garrity
Using the slow triangle map (a type of multi-dimensional continued fraction algorithm), we exhibit a method for generating any number of new identities for subsets of integer parti…
On integer partitions and continued fraction type algorithms
Wael Baalbaki, Claudio Bonanno, Alessio Del Vigna +2
We show that the additive-slow-Farey version of the traditional continued fractions algorithm has a natural interpretation as a method for producing integer partitions of a positiv…
Functional analysis behind a Family of Multidimensional Continued Fractions: Part II
Ilya Amburg, Thomas Garrity
This paper is a direct continuation of "Functional analysis behind a Family of Multidimensional Continued Fractions: Part I," in which we started the exploration of the functional…
Review of Steven H. Weintraub's Differential Forms: Theory and Practice
Thomas Garrity
Not only a review of Weintraub's Differential Forms: Theory and Practice but also a discussion of why differential forms should be taught to undergraduates and an overview of some…
Functional Analysis behind a Family of Multidimensional Continued Fractions: Part I
Ilya Amburg, Thomas Garrity
Triangle partition maps form a family that includes many, if not most, well-known multidimensional continued fraction algorithms. This paper begins the exploration of the functiona…